Expand the determinant along the first row: $1 \begin{vmatrix} 2 & 1 \\ 1 & 3 \end{vmatrix} - 3 \begin{vmatrix} 3 & 1 \\ 2 & 3 \end{vmatrix} + 2 \begin{vmatrix} 3 & 2 \\ 2 & 1 \end{vmatrix}$.

Calculate the $2 \times 2$ determinants: $1(6 - 1) - 3(9 - 2) + 2(3 - 4)$.

$1(5) - 3(7) + 2(-1) = 5 - 21 - 2 = -18$.