So, f(x) = 3x² + 5x - 2 and you want to work out what f(x + 2) equals.
To find f(x +2) you simply replace every 'x' value in the equation by 'x + 2'
And so the equation would become:
f(x) = 3x² + 5x - 2
f(x + 2) = 3(x + 2)² + 5(x + 2) - 2
= 3(x + 2)(x + 2) + 5x + 10 - 2
= 3(x² + 2x + 2x + 4) + 5x + 8
= 3(x² + 4x + 4) + 5x + 8
= 3x² + 12x + 12 + 5x + 8
= 3x² + 17x + 20
Which is the answer you wanted.