To solve the equation, let's simplify each side step by step:

7/4 - y x 7/12 = 1/2 + 2/3

First, let's find a common denominator for the fractions on the right side of the equation. The common denominator for 2 and 3 is 6.

7/4 - y x 7/12 = 3/6 + 4/6

Next, let's simplify the fractions on the right side of the equation:

7/4 - y x 7/12 = 7/6

Now, let's simplify the left side of the equation. To do this, we need to find a common denominator for 4 and 12, which is 12.

7/4 - y x 7/12 = 7/6

Multiplying the fractions on the left side:

(7 x 3)/(4 x 3) - y x 7/12 = 7/6

21/12 - y x 7/12 = 7/6

Now, let's combine the fractions on the left side:

(21 - y x 7)/12 = 7/6

To get rid of the denominator, we can cross-multiply:

6(21 - y x 7) = 7(12)

126 - 6y x 7 = 84

126 - 42y = 84

Now, let's isolate the variable y by moving the constant term to the other side:

-42y = 84 - 126

-42y = -42

Finally, divide both sides by -42 to solve for y:

y = -42/-42

y = 1

Therefore, the solution to the equation is y = 1.