The equation of line A is y = 6x -4. The equation of line B is 2y - 12x + 14 = 0. Are these two lines parallel?

Line A has a gradient of 6, because it is in the form y = mx + c, where m=6.
Line B can be rearranged to y= 6x - 7, so the gradient is also 6.
The gradient of both lines is the same, so they are parallel.