Question Let $x = [X_1, X_2, X_3, X_4]^T$ be a multivariate and normal random vector and $$ \mu = \begin{bmatrix} 0 \\ -1 \\ 2 \\ 0 \end{bmatrix}, \Sigma =\begin{bmatrix} 4 & 1 &0 & 2 \\ 1 & 4 & 3 & 0 \\ 0 & 3 & 9 & 3 \\ 2 & 0 & 3 & 9 \end{bmatrix}, $$
Find $Cov(X_1, X_2)$
Is it possible to find the Covariance of $X_1$ and $X_2$ by looking at these two matrices?
Presumably, the density function of the $\ x\ $ in your question is $$ \frac{\displaystyle e^{-(x-\mu)^T\Sigma^{-1}(x-\mu)}}{(2\pi)^2\sqrt{\det \Sigma}}\ , $$ in which case $\ \Sigma\ $ is the covariance matrix of $\ \big[X_1,X_2,X_3,X_4\big]^T\ $, and your surmise that $\ Cov\big(X_1,X_2\big)=\Sigma_{12}\ $ is correct.