To solve the equation, we will first simplify each term:

1/6 * 1/4x = 1/24x
-1/3 = -8/24
-3/8 = -9/24

Now, substitute these values back into the equation:

1/24x - 8/24 - 9/24 = 1/40

Combining like terms:

1/24x - 17/24 = 1/40

Now, we can solve for x:

1/24x = 1/40 + 17/24
1/24x = 3/120 + 85/120
1/24x = 88/120
x = 88/120 * 24
x = 88/5
x = 17.6

Therefore, the solution to the equation is x = 17.6.