Answer:
B
Step-by-step explanation:
The correct answer is B: let me provide some explanation. The phrase "even though my brother hates ping pong" isn't enough to be a sentence on its own. It isn't a complete thought. The reader is left thinking, even though what?
We call that a sentence fragment, or a dependent clause. You have to pair it with an independent clause in order to make the whole thing a sentence. This is done correctly in choice B.
Why not A: Semicolons are used to link two independent clauses. Example: I brush my teeth; I comb my hair.
Why not C: We've already learned that "even though my brother hates ping pong" isn't a full sentence, so don't strand it on its own!
Why not D: Technically, there should be a comma after ping pong here, because it's more than a 5-word clause. If you're not being picky, D could also work, but it's missing a comma.