To find the value of the expression A(b-4)-b(a-3) when a=2, b=1/3, we can substitute these values into the expression and simplify:

A(b-4)-b(a-3)
= A(1/3 - 4) - (1/3)(2-3)
= A(-11/3) + 1/3
= -11A/3 + 1/3

Now, since we are given the values of a=2 and b=1/3, we can substitute these into the expression we simplified:

-11(2)/3 + 1/3
= -22/3 + 1/3
= -21/3
= -7

Therefore, the value of the expression A(b-4)-b(a-3) when a=2, b=1/3 is -7.