Your answer would be false.
This is because although the circle is centered around (0, 2) as the first part of the equation, x² + (y - 2)² suggests, but as the equation equals 12, the radius of the circle must be √12.
√12 = 3.46, so around 3.5, and the radius of the circle pictured is 4, which we can see as the circle passes through the point (0, -2), which is 4 units away from the centre.
Therefore, the equation has the wrong radius and is therefore not the circle illustrated.
I hope this helps!