Answer
$$\eqalign{
& {\text{amplitude: }}\frac{1}{4} \cr
& {\text{period: }}3\pi \cr
& {\text{vertical translation}}:3{\text{ up}} \cr
& {\text{phase shift}}:{\text{none}} \cr} $$
Work Step by Step
$$\eqalign{
& y = 3 - \frac{1}{4}\cos \frac{2}{3}x \cr
& {\text{Rewrite the function}} \cr
& y = - \frac{1}{4}\left[ {\cos \frac{2}{3}\left( {x - 0} \right)} \right] + 3 \cr
& {\text{The function is written in the form }}y = a\cos \left[ {b\left( {x - d} \right)} \right] + c \cr
& \underbrace {y = - \frac{1}{4}\left[ {\cos \frac{2}{3}\left( {x - 0} \right)} \right] + 3}_{y = a\cos \left[ {b\left( {x - d} \right)} \right] + c} \cr
& {\text{with:}} \cr
& a = - \frac{1}{4},\,\,\,b = \frac{2}{3},\,\,\,\,d = 0,{\text{ }}c = 3 \cr
& \cr
& {\text{The amplitude is given by }}\left| a \right|,\,\,\,\,\left| a \right| = \left| { - \frac{1}{4}} \right| = \frac{1}{4} \cr
& {\text{The period is given by }}\frac{{2\pi }}{b} = \frac{{2\pi }}{{2/3}} = 3\pi \cr
& {\text{The vertical translation is }}c = 3{\text{ up}} \cr
& {\text{The phase shift is }}d{\text{ translation is }}d = 0,{\text{ none}} \cr
& \cr
& {\text{amplitude: }}\frac{1}{4} \cr
& {\text{period: }}3\pi \cr
& {\text{vertical translation}}:3{\text{ up}} \cr
& {\text{phase shift}}:{\text{none}} \cr} $$
