Answer
The Amplitude is $2$
The Period is ${3\pi}$
The Horizontal shift is $\frac {\pi}{4}$ units to the right
See graph below.
Work Step by Step
For $y=a\sin c(x−h) + k$ $y =a \cos c(x−h) + k$,
Amplitude: $|a|$, Period: $\frac{2\pi} {|c|}$,
Horizontal Shift: h
The question asks for a graph, amplitude, period, and horizontal shift of the function.
Given $y = 2\sin (\frac{2}{3}x - \frac{\pi}{6})$
$y = 2\sin \frac{2}{3}(x - \frac{\pi}{4})$
The Amplitude is $|2| = 2$
The Period is $\frac{2\pi}{|\frac{2}{3}|} = {3\pi}$
The Horizontal shift is $\frac {\pi}{4}$ units to the right
See graph below.