I had the following problem on my test today and I supposedly got the wrong answer but I can't seem to find where I went wrong. Please let me know if you see an error in my work:

Find the distance between the given parallel planes: 4z= 6y- 2x(Plane A)

6z= 2 - 3x+ 9y (Plane B)

Let x = y = 0 on plane 6z = 2 - 3x + 9

6z = 2

z = 3

Thus we have the point (0,0,3) and to find the distance between this point on Plane B and Plane A there is the formula:

absolute value( a(x0) + b(y0) + c(z0) - D ) / sqrt(a^2 + b^2 + c^2)

plane A has: a = 2, y = -6, z = 4, d = 0

so, i did 2(0) - 6(0) + 4(3) = 12 / sqrt( 4 + 36 + 16)

12 / sqrt(56) and further reduced to 6/sqrt(14)

the computer assignment says this is wrong... any help is greatly appreciated.

Thanks in advance.