To solve this equation, we first need to simplify the left side:

(2/3 - x) * 1 1/2 = -3/4

To convert 1 1/2 to an improper fraction, we multiply the whole number (1) by the denominator (2) and add the numerator (1) to get 3/2:

(2/3 - x) * 3/2 = -3/4

Now we can distribute the 3/2 to both terms inside the parentheses:

(2/3 * 3/2) - (x * 3/2) = -3/4
(6/6) - (3x/2) = -3/4
1 - 3x/2 = -3/4

Now we can multiply both sides by 2 to get rid of the fraction:

2(1 - 3x/2) = 2(-3/4)
2 - 3x = -6/4
2 - 3x = -3/2

Next, we can isolate the variable x by subtracting 2 from both sides:

-3x = -3/2 - 2
-3x = -3/2 - 4/2
-3x = -7/2

Finally, we divide by -3 to solve for x:

x = (-7/2) / -3
x = 7/6

Therefore, the solution to the equation (2/3 - x) * 1 1/2 = -3/4 is x = 7/6.