How to solve. Y=-4 (x-2) squared+4

What do you mean, "solve"?

y = - 4 (x-2) ² + 4

the line is a parabol with a maximum (2; 4)

it's roots are - 4 (x-2) ² + 4 = 0 = > (x-2) ² = 1 = > x-2 = 1 = > x = 3

=> x-2 = - 1 = > x = 1

symetrical axe: x = 2

is that all you need?