In the function f (x) = 4 (x² - 6x + ___) + 20, what number belongs in the blank?

If the brackets need to be a square term of the form (x+h) ^2

then

just half the co-efficient of x term and square it.

So here it will be

(-6) / 2 = - 3

squaring it, (-3) ^2 = 9

so 9 is what goes in the blank to make the bracket () of the form (x+h) ^2