What all can be embroidered with a 4 by 4 hoop? I have a Brother SE-400.

You can stitch any 4x4 or smaller designs. But, it is better to use the smallest hoop you have to do small designs if you have a smaller hoop.

You can do larger designs, but you'd have to use a process called "splitting" to divide up the designs into several parts. You have to reposition the fabric in the hoop and get it lined up perfectly too. It helps if you have software that will split this for you. If you are a beginner, I wouldn't try splitting until you are quite confident in your skills.

Make sure the design is smaller than 100mm x 100mm for your hoop.

I have 2 janomes and both 4x4 hoops for them are actually larger than the 4x4 brother hoops.

Welcome to Cute
You can embroider any design that is less than 4" square. When you purchase a design you have to watch the size.