To solve this equation, we will first simplify the expression on the left side of the equation.

(x-2)/3 * 3/5 = 2 1/12

First, distribute the 3/5 to (x-2):

3/5 * (x-2) = (3x - 6)/5

Now the equation becomes:

(3x - 6)/5 = 2 1/12

To convert 2 1/12 to an improper fraction, we multiply 2 by 12 and add 1 to get the numerator:

(2 * 12) + 1 = 24 + 1 = 25

Therefore, 2 1/12 = 25/12

So the equation is now:

(3x - 6)/5 = 25/12

To solve for x, we can cross multiply:

5 25 = 3 (3x - 6)

125 = 9x - 18

Adding 18 to both sides:

125 + 18 = 9x

143 = 9x

Divide by 9 to get x by itself:

143/9 = x

Therefore, x = 143/9 = 15.888888888 = 15 and 8/9

The solution to the equation is x = 15 and 8/9.