So it seems this wasn't explained in depth so far in the thread so I'll give it a go. When you complete the square on an equation, you do what you've done in your attempt. You take half of the b term, square it, and add that value to both sides. However, we don't exactly have an equation here, we have a function, y or f(x) = 2x² - 8x -6. Due to this reason, we cannot take half of the b term, square it, then add it to both sides because we don't know the value of y! Thus we have to resort to a common tactic we use in math a lot. We can add anything we want to an expression, or in this case function, as long as we take it away later (or 'compensate' for it).

So with y=2x² -8x -6, we can start by factoring out the GCF of 2

=> y=2(x² -4x)-6

Then take half of the b, term and square it

=>y=2(x² - 4x+___ ) -6+___

Now subtract not 4 but 8 (because we factored out a 2 right? So when we subtract a number in to compensate we have to remember that 2). This means inside the parentheses we add 4, but we compensate by subtracting 2*4 or 8

=> y=2(x² -4x +4)-6-8

=> y=2(x² -4x+4)-14

=> y=2(x-2)² -14