Answer
${\text{Shell method}}$
Work Step by Step
$$\eqalign{
& {\text{Let:}} \cr
& y = 4 - {e^x} \to x = \ln \left( {4 - y} \right) \cr
& {\text{Let }}y = 0 \cr
& 4 = {e^x} \cr
& x = \ln 4 \cr
& {\text{We have the following methods to find the volume:}} \cr
& {\text{*Shell method about the }}y{\text{ - axis:}} \cr
& V = \int_a^b {2\pi x\left( {f\left( x \right) - g\left( x \right)} \right)} dx \cr
& and \cr
& {\text{*Disk method about the }}y{\text{ - axis:}} \cr
& V = \int_c^d {\pi p{{\left( y \right)}^2}} dy \cr
& {\text{It is more convenient apply the Shell method}}{\text{ because}} \cr
& {\text{the integrand is in the form }}4 - {e^x}{\text{ which is easier }} \cr
& {\text{that}}\ln \left( {4 - y} \right){\text{ to integrate}}{\text{. Then}} \cr
& V = \int_0^{\ln 4} {2\pi x\left( {4 - {e^x}} \right)} dx \cr} $$
