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:
$\begin{bmatrix}1&1\\1&1\end{bmatrix}\begin{bmatrix}1&0\\0&2\end{bmatrix}=\begin{bmatrix}1&2\\1&2\end{bmatrix}$
$\begin{bmatrix}1&0\\0&2\end{bmatrix}\begin{bmatrix}1&1\\1&1\end{bmatrix}=\begin{bmatrix}1&1\\2&2\end{bmatrix}$
There are two symmetric matrices given of size $2\times2$ and $AB != BA$. Therefore (C) is not a correct option!