Are the two equations - 6 + y = 2x and 2y - 4x = 12 dependent?

Yes they are linearly dependent, essentially the same equation.

Start from one of them:

-6 + y = 2x

Move things around:

y - 2x = 6

Multiply both sides by 2,

2y - 4x = 12

That's the second equation, which we've shown is equivalent to the first, so they're linearly dependent.