How do you make a home bomb in xbox360 edition?

You don't need to add what version you are playing, because you've asked your question in the Minecraft for Xbox 360 Q&A, which means you are asking your question for the Xbox 360 version of Minecraft.

I'm not sure what you mean by "home bomb." I'm going to assume you mean to ask how to rig a house to explode. You will need TNT, which is craftable using Gunpowder and Sand. More TNT make a larger explostion. You will also need some way to trigger the TNT. You can light it on fire, but that would require you to stand close to the explosion. I would suggest hiding TNT behind wool or wood, and use the flammable block as a fuse. This will hide TNT. You could also rig the TNT using combinations of Levers, Buttons, Pressure Plates, and Redstone.

One of the most common hiding places for TNT is under the floor, which makes Pressure Plates a good choice, however Pressure Plates are easy to spot, so either hide them around a corner or make them seem useful for some other reason. You could also hide TNT in the ceiling, behind the walls, or in the furniture (if you build elaborately).

I will say that I do not condone griefing, and I hope that whatever you do with this information you do with a consenting friend, or in your own private world.