Step 1 :Given the matrix \[\left|\begin{array}{ll} -3 & 2 \\ -1 & 2 \end{array}\right|\]
Step 2 :The determinant of a 2x2 matrix \[\left|\begin{array}{ll} a & b \\ c & d \end{array}\right|\] is calculated as ad - bc.
Step 3 :In this case, a = -3, b = 2, c = -1, and d = 2.
Step 4 :So, the determinant would be (-3*2) - (2*-1) = -4.
Step 5 :Final Answer: The value of the determinant is \(\boxed{-4}\)