Think of an independent clause as a mini sentence, it has a subject and a verb and makes complete sense on its own. Problems arise when two such mini sentences are placed together without a linking word like and or but. Writers then have three common punctuation choices, and only one of them actually does the job correctly.
Using just a comma between two independent clauses is called a comma splice, and it is considered incorrect in standard written English because a comma is too weak a mark to hold two complete thoughts together on its own. Using a period turns the two clauses into two separate, unconnected sentences, which defeats the purpose since the question specifically asks how to connect them, not separate them. A colon has a different job altogether, it signals that what comes next explains, lists, or elaborates on what came before, so it is not a general-purpose connector for two equal independent clauses.
The semi-colon is built exactly for this situation, it is strong enough to separate two complete clauses grammatically while still showing the reader that the ideas are closely related and belong in one sentence. That is why the answer is option 2, semi-colon.