Simplify (6–√ 2)raised to power 2− (6–√−2)raised to power 2?

I assume you mean

(6-√2)^2 - (6-√-2)^2
or
(6-√2)^2 - (6-√2 i)^2
= 36 - 12√2 + 2 - (36 - 12√2 i - 2)
= 4-12√2 - 12√2 i
Now, if you instead meant
(6-√2)^2 - (6+√2)^2 then that would be a difference of two squares, giving
((6-√2)+(6+√2))((6-√2)-(6+√2))
= 12(-2√2)
= -24√2