A symmetric matrix is a square matrix that is equal to its transpose.
(AB)' = B'A' =BA as Both $A$ and $B$ are symmetric matrices, hence $B' = B$ and $A'=A$
So, (D) is correct option!
Why is $(C)$ not correct option? see the following example:
There are two symmetric matrices given of size $2$x$2$ and $AB != BA$. Therefore (C) is not a correct option!