Here are the corrected run-on sentences using methods 1 and 2:
Method 1:
2. I forgot my homework at home. I will have to do it tonight.
4. She went to the store she needed milk and bread.
6. He walked to school he wanted exercise.
8. I finished my assignment I am going to relax.
Method 2:
1. I forgot my homework at home, but I will have to do it tonight.
3. She went to the store, and she needed milk and bread.
5. He walked to school, so he wanted exercise.
8. I finished my assignment, so I am going to relax.