It's been too long since I did an old chapter recap.
If you can't infer from the above sentence that I am in fact about to do another old chapter recap, then you need to work on your inferring skills.
1. I think this cover is made worse by the fact that it's clear that Amano is actually trying here. You can see in the way that Yamamoto is posing and Gokudera is staring off into the angsty abyss that this was a sincere attempt on her part to make them look attractive. Unfortunately, though, the fact that Gokudera apparently stole his clothes from a hobo on the beach tends to ruin whatever effect she was going for. This coupled with the fact that Yamamoto's hair, shirt, and pants are all several sizes too big and I swear to God Amano just has NO IDEA how to draw elbows at all, and this becomes one of those really awkward pictures that everyone just likes to skim quickly over in the photo album and pretend like it doesn't exist.
2. So anyway, this chapter begins with Yamamoto hitting on his failure buddy Tsuna (and he really does call him that, that is canon) while Gokudera dramatically clenches his fist in a jealous rage. Reborn, sensing an opportunity for mischief, decides to hold an entrance test to determine if Yamamoto is really VONGOLA MATERIAL, and Tsuna is all NOOOOOOOO, but like that's ever done him any good.
3. So Gokudera goes to challenge Yamamoto with the staredown of all staredowns, coming at him AGAIN AND AGAIN from DIFFERENT ANGLES!!1 and judging him for all he's worth. Yamamoto responds by suggesting that Gokudera should drink some milk because CALCIUM IS GOOD FOR YOU, and I think this was the exact point when I decided that I loved them. That calcium panel. That is what put them over the top.
Tsuna shows up just in time to prevent a homicide, and inadvertently introduces Yamamoto to his new best friend Reborn. They hit it off fabulously, and we get the first mention of the mafia game and our second indication in this chapter that Yamamoto may in fact be a few fries short of a Happy Meal.
4. Reborn explains that Tsuna is the tenth boss of the Vongola family, and Tsuna alternates between being horrified at Reborn's forwardness and jellin' over the fact that barely two seconds after they've met, Yamamoto is already Reborn's favorite. But Yamamoto cuts his tantrum short by declaring, in the first genuinely sexy panel I think anyone in this manga has had, that he wants in on this mafia thing. ALL RIGHT, NOW WE'RE GETTING TO BUSINESS.
5. Reborn helpfully explains that if Yamamoto doesn't pass the family entrance test, he'll die, and Yamamoto laughs and pats him on the head because it's so cute when little kids precociously threaten their elders' lives. |D Reborn promptly begins throwing an assortment of deadly objects at him, to Gokudera's unabashed delight. Thankfully this was a comedic chapter, so we don't have to spend too much time pondering the implications of Gokudera so thoroughly enjoying the idea of his innocent classmate getting impaled to death. IT'S OKAY, THIS WAS PRE-FIREWORKS AFTER ALL, things weren't all dandelions and Jesusflakes just yet.
6. Teeheehee, would you just look at this middle panel? I can't think of a more perfect way to sum up the essential differences between Tsuna and Yamamoto than by comparing their faces in this situation. A BABY IS THROWING KNIVES AT THEM, and Yamamoto is all, ">|D" whereas Tsuna has the substantially more appropriate reaction of, "D8!!!!!!" Heh.
7. SUDDENLY, LAMBO APPEARS! Because apparently Amano wasn't satisfied with the level of craziness she had built up thus far. But of course, he's ignored as per usual, so he responds by whipping out a missile launcher (PERFECTLY REASONABLE), and blowing shit up. I would just like to note that his response to not killing Tsuna and Yamamoto is to narrow his brow and state regretfully while holding the still-smoking launcher, "Darn, lacked ten more meters," which is the single most hardcore thing any character has ever said or done in this series, and it was FUCKING LAMBO who said it and it was the FUCKING FIVE-YEAR-OLD VERSION, and holy shit. DID THAT REALLY JUST HAPPEN. WHY DO I HAVE NO MEMORY OF THIS. All this time and I never recalled that Lambo was secretly a complete badass.
8. Reborn for his part is also disappointed that no one has managed to die yet, and starts shooting a machine gun at them while also instructing Gokudera to let loose with his bombs. Actually, he tells Gokudera to "go loose" while thinking about killing Yamamoto, so make what you will of that.
Meanwhile, TYL!Lambo appears and seems to instinctively understand that his younger self summoned him for the purposes of murder, so he does his whole THUNDER SET thing in the midst of all this chaos, and to make a long story short, things explode. Gokudera has a belated moment of self-awareness in which he acknowledges that he MAYBE POSSIBLY just MIGHT HAVE overdone it A BIT, but it's all good because Yamamoto is a superhero.
9. Gokudera reluctantly allows Yamamoto to be in the family on account of Yamamoto saving Tsuna from a violent terrible death, but tells him in no uncertain terms that the one who's gonna be the Tenth's right hand is HIM, BITCH, so you'd best know your place. Yamamoto decides at this moment that a) this guy is hilarious and b) he would like nothing more than to instigate a rivalry with him right on the spot, so he does, and thus an amazing mafia bromance was born. Aww.
10. So in the end, everything was resolved, and as for Lambo, I can only assume he vanished off into the sunset and traveled far and wide and ended up training a young Kawahira in the ways of the enigmatic badass, before one day being ambushed by his longtime nemesis Jason Bourne and suffering a traumatic brain injury that gave him amnesia and tragically altered his personality into a namby-pamby failure, and Kawahira wept and swore to one day get revenge, but in the meantime Lambo would be safer with the Vongola, and so he sent him back to them, unaware of his true identity as an awesome guy.
The end.