Answer:
It should be a compound sentence, with the following being your independent and dependent clause.
INDEPENDENT: We browsed the gift shop for souvenirs.
DEPENDENT: After we ate lunch at the Japanese tearoom.
Explanation as to why:
Very simple, compound sentences have two parts in the sentence, commonly separated by a comma and two separate thoughts.
To help you decide whether something is a dependent or independent clause, read the sentence in your head and see it if sounds like it makes sense, if it doesn't, that means its your dependent. It's because it DEPENDS on another thought to complete it. To identify your independent, it usually sounds like a complete thought with a start and an end.
Hopefully this helps you understand it better!
