Parallelogram Verification: Quadrilateral with Sides 12 and Diagonals 6

We need to determine if quadrilateral $ABCD$ is a parallelogram based on the side lengths and properties provided. For a quadrilateral to be a parallelogram, one way is to confirm whether both pairs of opposite sides are congruent.

We are given the following side lengths:

• $AB = 12$
• $CD = 12$
• $AC = 6$
• $BD = 6$

Let's apply the theorem: If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.

Checking the pairs of opposite sides:

• Side $AB = 12$ and side $CD = 12$. Thus, $AB = CD$.
• Side $AC = 6$ and side $BD = 6$. Thus, $AC = BD$.

Since both pairs of opposite sides are congruent, quadrilateral $ABCD$ satisfies the parallelogram condition.

Therefore, the answer to the question is that the quadrilateral is indeed a parallelogram, and the correct choice is:

Yes.