First, distribute the square root of 2 to both terms inside the parentheses:

√2(3x) - √2(4) = 6

Simplify:

3√2x - 4√2 = 6

Now we want to isolate the variable x. Add 4√2 to both sides:

3√2x = 6 + 4√2

3√2x = 6 + 4√2

Divide both sides by 3√2:

x = (6 + 4√2) / 3√2

x = 2 + (4/3)√2

So the solution is x = 2 + (4/3)√2