We find the y-intercept of 2x + 3y = 15 by letting x = 0 in that equation, and then solving for y. This gives 3y = 15, or y = 5. A handy way to find the equations of lines perpendicular to a given line is to reverse the x- and y-coefficients and simultaneously change the sign of one of them. Thus, a line perpendicular to ax + by = c is bx - ay = d. Doing this to 3x - 4y = 12 produces 4x + 3y = d. To find d, we use the fact that the line has a y-intercept of (0,5), so that 3*5 = d, or d = 15. Hence, the equation of the desired line is 4x + 3y = 15.
