Ah yes, the other boxes. Each for a member of your friend group. They each go into a row of your duck chart.
As mentioned prior, your sylladex is displayed alongside the ducks to which the item is to correspond with during the minigame. As shown here, the ducks are very difficult to distinguish, as all three of them are pink with pink heads and pink feet. Probably the only thing to distinguish them is one of them has a lighter head and an other has a brighter coat. Luckily, distinguishing isn't the goal of the game, so there's a line that points from one duck to the corresponding duck on the game. Also, you can turn off ducks if you really don't want to confuse yourself and get the wrong item.
The boxes enter your Sylladex and you make a mental note for yourself to give the gifts to your respective friends when you next meet them. Thinking about that makes you happy and hopeful that you will be able to give your friends the items and they will be happy too. Happiness is easy for you, but you can understand why it isn't for others. As mentioned about a thousand pages ago, you aren't very quick to getting angry about anything. This is why you always seem to be, and usually are, happy. It's a trait that has gotten you into some trouble because some jerks who think highly of themselves or something come up to you expecting you to be upset at their appearance or whatever, and then they get conscious about their inability to project fear, and then they beat you up.
You don't choose to always be happy, sometimes, you want to feel sad, or want to feel mad, but it's hard when all you know is mirth. You've been getting a little better at that since your mother died, but it's been a rough progression. You often worry that if you work too hard at it, you won't be able to be happy anymore, but that's only fleeting passions of remission.