I don't understand this question

How would you explain to your friend why the quotient of x*6 and x^2 is x^6 Remember your friend is questioning the rule, so you just cannot say it is the rule.

first of all if you meant it the way you typed it ...

(x*6)(x^2) = 6x^3

you probably meant
"the product of x^6 and x^2" which would be x^8

x^6 = xxxxxx
x^2 = xx
so
(x^6)(x^2) = (xxxxxx)(xx) = xxxxxxxx = x^8