To solve the first equation, 64/72 = (7y+3)/9, we can first simplify the left side by dividing both the numerator and denominator by their greatest common factor: 8.

64/72 = 8/9

Now, we can write the equation as:

8/9 = (7y+3)/9

Now, we can solve for y:

8 = 7y + 3
7y = 5
y = 5/7

Therefore, the solution for the first equation is y = 5/7.

To solve the second equation, 53/4 = 212/(6y-8), we can rearrange the equation to isolate the variable:

53/4 = 212/(6y-8)

Now, cross multiply to get rid of the fraction:

53(6y-8) = 4(212)
318y - 424 = 848

Now, solve for y:

318y = 1272
y = 1272/318
y = 4

Therefore, the solution for the second equation is y = 4.