Write an equation of a sine curve with amplitude 4 and period = 3pi/2

We have the equation

y  = Asin (Bx)

The amplitude  =   A   = 4   

Finding B   is a little tricky.....we want to  solve this  :

2pi / Period  = B

2pi  / [ 3pi / 2 ]  = B

4pi / 3pi  = B

(4/3)  = B

So...the equation becomes

y  = 4sin (4/3 x)

Here's the graph for one period   :  https://www.desmos.com/calculator/ncw51ksw5x