So basically we are combining the different clauses to make a coherent sentence. It's a lot easier than it looks, I'll show you:

#20: Though the grass was already cut, Kate, an over-in dustrious kid, offered to mow the lawn for five dollars.

#21: While waiting for his train to arrive, Baxter noticed a beautiful young woman who was looking for someone to help her with her bags.

Basically you have to reposition the sentences until they sound gramatically correct. Just take a few minutes and review the changes made and apply this in the other questions for your homework.