Answer
$$24$$
Work Step by Step
$$\eqalign{
& \int_{ - 2}^2 {\int_3^6 {\int_0^2 {dxdydz} } } \cr
& {\text{Integrate with respect to }}x \cr
& \int_{ - 2}^2 {\int_3^6 {\left[ x \right]_0^2dydz} } \cr
& \int_{ - 2}^2 {\int_3^6 {\left( {2 - 0} \right)dydz} } \cr
& \int_{ - 2}^2 {\int_3^6 {2dydz} } \cr
& {\text{Integrate with respect to }}y \cr
& \int_{ - 2}^2 {\left[ {2y} \right]_3^6dz} \cr
& 2\int_{ - 2}^2 {\left( {6 - 3} \right)dz} \cr
& 2\int_{ - 2}^2 {3dz} \cr
& 6\int_{ - 2}^2 {dz} \cr
& {\text{Integrate with respect to }}z \cr
& 6\left[ z \right]_{ - 2}^2 \cr
& = 6\left( {2 + 2} \right) \cr
& = 24 \cr} $$
