You want to isolate one of the variables (x or y) so you can plug it into the other equation. The easiest one is isolating the 2nd equation.
3x² - 16x + 13 - y = 0 Add y on both sides
3x² - 16x + 13 = y
You can use this and plug it into the first equation
y - 12x + 15 = 3x²
(3x² - 16x + 13) - 12x + 15 = 3x²
3x² - 16x + 13 - 12x + 15 = 3x² Combine like terms
3x² - 28x + 28 = 3x² Subtract 3x² on both sides
-28x + 28 = 0 Add 28x on both sides
28 = 28x Divide 28 on both sides
1 = x
Now that you know x, you can plug it into either of the equation to find y
3(1)² - 16(1) + 13 - y = 0
3 - 16 + 13 - y = 0
-y = 0 Divide -1 on both sides
y = 0
x = 1, y = 0