you know that 3 is a generator for U(10), good. that means if f:U(10)-->Z4 is given by f(3) = 2, you should be able to calculate the other images of f by taking images of powers of 3:

f(9) = f(3^2) = f(3) + f(3) = ?

f(7) = f(3^3) = f(3) + f(3) + f(3) = ?

f(1) = f(3^4) = f(3) + f(3) + f(3) = ?

is f bijective?