Option C: $y = -3$
A line parallel to the x-axis has equation $y = k$. Since it is 3 units below the x-axis, $k = -3$, giving $y = -3$.
Lines parallel to the x-axis are always of the form $y = \text{constant}$. "Below the x-axis" means the y-value is negative. Options A and B ($x = 3$, $x = -3$) are lines parallel to the y-axis, so they are wrong. Option D ($y = 3$) is above the x-axis, not below.