Expanding the given equations, we get:

4(2x - y + 3) - 3(x - 2y + 3) = 48
=> 8x - 4y + 12 - 3x + 6y - 9 = 48
=> 5x + 2y + 3 = 48
=> 5x + 2y = 45 .....(1)

3(3x - 4y + 3) + 4(4x - 2y - 3) = 48
=> 9x - 12y + 9 + 16x - 8y - 12 = 48
=> 25x - 20y - 3 = 48
=> 25x - 20y = 51 .....(2)

Now, we have to solve the two equations (1) and (2) simultaneously to find the values of x and y.

Multiplying equation (1) by 5 and equation (2) by 2, we get:

25x + 10y = 225 .....(3)
50x - 40y = 102 .....(4)

Adding equation (3) and equation (4), we get:

75x - 30y = 327
=> 5(5x + 2y) = 3(5x - 2y) = 327
=> 25x + 10y = 327

Therefore, the solution for x = 51/5 = 10.2 and y = 29/20 = 1.45.