If I put a sentence here listing the dependent and independent clauses within the sentence can you tell me if I am correct. Here is the sentence.

I have read several fairy tale collectionthat include th Cinderella story, but my favorite is a book that belonged to my great-grand mother.

I think this this a compound sentence because it has two independent clauses and a cordinating conjunction.
thanks

There are also 2 dependent clauses in there. What do you call a compound sentence (yes, that's correct) that also has dependent (or subordinate) clauses in it?

Yes, you are correct. The sentence you provided is a compound sentence because it consists of two independent clauses joined by a coordinating conjunction. The independent clauses are:

1. "I have read several fairy tale collections that include the Cinderella story."
2. "My favorite is a book that belonged to my great-grandmother."

They are connected by the coordinating conjunction "but." Well done!