What kind of sentence is the following: wait for me to come home.

Hello there!

The answer to this question is imperative sentence.

An imperative sentence doesn't seem to have a direct subject; however, the subject of each imperative sentence is "you". It's like a command. If your mom was to say, "Turn off the TV", she would be telling you to turn off the TV. That's an example of an imperative sentence.

In this question, "wait for me to come home" is an imperative sentence because it is the command of telling you to wait without actually saying "you". Hope this helps! :)