Which of the reconstruction amendments guarantees african Americans the right to vote?

Answer: 15th Amendment

Explanation:

The 15th Amendment states that "The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude."

Basically, it states that African Americans cannot be denied the right to vote just because they are African Americans, which is what you are looking for.