Anwer: (2) 3 pairs

Solution

3xy-4x = 3y

x= 3y/(3y-4)

x= 1+ 4/(3y-4)

now x will be integer when 3y-4 is a factor of 4 (both positive and negative values)

hence 3y-4 = 1 , 2 , 4 , -1, -2 , -4 

y will be 5/3, 2, 8/3, 1, 2/3, 0 

hence y will be integer on 3 of those values.

Hence there are 3 integer pairs of (x,y) that satisfy the above equation.