Answer
$$ - 1$$
Work Step by Step
$$\eqalign{
& {\left. {\frac{d}{{dx}}\left[ {2x - 3g\left( x \right)} \right]} \right|_{x = 4}} \cr
& {\text{Calculate the derivative}} \cr
& \frac{d}{{dx}}\left[ {2x - 3g\left( x \right)} \right] = 2 - 3g'\left( x \right) \cr
& {\text{Evaluate at }}x = 4 \cr
& {\left. {\frac{d}{{dx}}\left[ {2x - 3g\left( x \right)} \right]} \right|_{x = 4}} = 2 - 3g'\left( 4 \right) \cr
& {\text{From the table we know that }}g'\left( 4 \right) = 1 \cr
& {\left. {\frac{d}{{dx}}\left[ {2x - 3g\left( x \right)} \right]} \right|_{x = 4}} = 2 - 3\left( 1 \right) \cr
& {\left. {\frac{d}{{dx}}\left[ {2x - 3g\left( x \right)} \right]} \right|_{x = 4}} = - 1 \cr} $$
