Given matrices $A, B, C' \in \Bbb R^{2 \times 6}$, where $'$ denotes matrix transposition, and matrix $L \in \Bbb R^{2 \times 2}$, how can one solve the following linear matrix equation in $X \in \Bbb R^{2 \times 2}$?

$$ ACXC'A' - BCXC'B' = L $$

$X$ is a covariance matrix that should be positive definite or semidefinite. Is there any standard solution to ensure getting correct values?