Answer:
4. After walking my dogs, (I SAT DOWN) to do my homework assignment.
Step-by-step explanation:
To answer this question we need to know a definition of a clause.
A clause is a group of words that consists of a subject and a verb. A clause is different from a phrase, as the phrase does not contain a subject, a verb, or a complete thought (in the kitchen, two big cats, etc).
1. My (TWO LARGE DOGS HAPPILY) chased each other around the backyard - not a clause.
These words in parentheses create a phrase, but not a clause. It doesn't have a complete thought or a verb.
2. Because of their size, my dogs must be (FED THREE MEALS DAILY) - not a clause.
These words in parentheses create a phrase, but not a clause. It doesn't have a complete and a subject.
3. I wash my dogs (OUTSIDE NEAR) the garage once every two weeks - not a clause.
This is a phrase; it doesn't have a subject, a verb, and a complete thought.
So, only sentence 4 is a clause. It has a subject, a verb, and it could stand alone as it has a complete thought.
I hope it helped you :)