1/ Let's isolated y for both equations
5x + 2y = 6 becomes y = -5/2x +3
3x - ay = 4 becomes y = 3/ax - 4/a
2/ The slope of each lines is m, which is the coefficient in front of the x (here -5/2x & 3/ax)
3/ So we just need to solve for these 2 coefficient (m) being equal in order for the 2 lines to be parallel.
meaning we want to find a for : -5/2 x = 3/a x
4/ Let's solve then:
cancel out the two x on each side
-5/2 = 3/a
isolate a:
a = - 6/5