Parallelogram Verification: Quadrilateral ABCD with Sides 15, 12, 7, and 8

To determine whether the quadrilateral ABCD is a parallelogram, we must establish whether both pairs of opposite sides are equal. In a parallelogram, this criterion is met: the opposite sides are congruent.

First, we compare the lengths of the opposite sides:

• Length $AB = 15$ and length $CD = 12$. These two sides are not equal.
• Length $AC = 8$ and length $BD = 7$. These two sides are also not equal.

Since neither pair of opposite sides is equal, quadrilateral ABCD does not satisfy the conditions for being a parallelogram.

Therefore, the solution to the problem is that quadrilateral ABCD is not a parallelogram.

$\boxed{\text{No}}$