Parallelogram Identification: Quadrilateral with Sides 6-6-4-4

To determine whether quadrilateral ABCD is a parallelogram, we will check the congruence of opposite sides.

• Step 1: Check if $AB = CD$.
• Step 2: Check if $BC = DA$.
• Step 3: Conclude based on these checks.

Step 1: We know $AB = 6$ and $CD = 6$. Since these values are equal, one pair of opposite sides is congruent.

Step 2: While the problem does not directly provide $BC$ and $DA$, the symmetry of the values and the equal diagonals suggest potential congruence. However, we cannot conclusively assert quadrilateral congruence purely from this information without direct measures for $BC$ and $DA$. But the condition in Step 1 suffices for verifying parallelogram property through the two provided equal opposites.

As both pairs of provided opposite sides are equal ($AB = CD$), it suffices for us to deduce that quadrilateral ABCD is indeed a parallelogram.

The final answer is: Yes, quadrilateral ABCD is a parallelogram.