The correct answers are Please take out the trash; it is starting to smell like a swamp in here. and You need to clean up this mess in the kitchen before dinnertime.

"Take out" means to remove something from inside to outside (like the trash).

"Clean up" means to make a place neat and tidy.

You "put away" (store in their proper place) clean clothes, rather than "throw away" (discard) them.

You "throw away" things in the trash can, rather than "put away" dishes there.