How many distinct triangles can be formed for which m∠a = 75°, a = 2, and b = 3?

We are given
m∠A = 75 deg
a = 2
b = 3

Apply the Law of Sines.
sin(B)/b = sin(A)/a
sin(B)/3 = sin(75)/2
sin(B) = (3*sin(75))/2 = 1.45

The value of the sin function cannot exceed 1.
This means that the triangle cannot exist.

No distinct triangles