#### Answer

The amplitude is $16.5$, the period is $12$, the vertical translation is $67.5$ units up and the phase shift is $4$ units to the right.

#### Work Step by Step

We first write the equation in the form $y=c+a \cos [b(x-d)]$. Therefore, $y=16.5\sin [\frac{\pi}{6}(x-4)]+67.5$ becomes $y=67.5+16.5\sin [\frac{\pi}{6}(x-4)]$.
Comparing the two equations, $a=16.5,b=\frac{\pi}{6},c=67.5$ and $d=4$.
The amplitude is $|a|=|16.5|=16.5$
The period is $\frac{2\pi}{b}=\frac{2\pi}{\pi/6}=12$
The vertical translation is $c=67.5$
The phase shift is $|d|=|4|=4$
Therefore, the amplitude is $16.5$, the period is $12$, the vertical translation is $67.5$ units up as $c$ is more than zero and the phase shift is $4$ units to the right since $d$ is more than zero.