I need to graph this equation y=(3/2)sin(3x+2ð)-3. What would the primary interval be for this problem and how would it appear on a graph?

I will assume that the unusual symbol is π and

y=(3/2)sin(3x+2π)-3
= (3/2)sin 3(x+2π/3)-3

not sure what you mean by "the primary interval" but your curve has a period of 2π/3 or (120°)
and y = (2/3) sin 3x is shifted 2π/3 units to the left, and then 3 units down