State the amplitude, period, phase shift, and vertical shift of the function y= -3 (1/2x- 2/3 pi)-4

Answer 1

I have a feeling that you have a typo and this is supposed to be either a sine or cosine function
Assuming I am correct .....
for any sine function in the form:
y = a sin (k(Ø + d)) + c

|a| is the amplitude
the period is 2π/k
the phase shift is d units to the left, or -d units to the right
the vertical shift is c

apply to your equation.

the only tricky part I see is in the period
change your equation to
y = -3sin((1/2)(x - 4/3) ) - 4
so the phase shift is 4/3 units to the right.