Here is the item again:
When Minori left Japan to study in the United States, she thought that she
would miss her mother's delicious cooking,
however, after her first taste of a bacon cheeseburger, she did not
care if she ever returned home.
She thought ... begins a complete sentence. She did not care ... starts another complete sentence. Notice that these two sentences have no punctuation stronger than a comma connecting them, thus creating a comma splice, a major sentence error.
To fix the problem, you could put a semicolon after cooking. A semicolon is a strong enough mark of punctuation to connect two complete sentences.