The normal to the curve y(x²)(x³) = x + 6 at the point where the curve intersects the y-axis passes through the point. (12, 12), (-2, -2), (12, -3), (12, 13)

Given y(x²)(x³) = x + 6 ⇒ y = x + 6/(x²)(x³)
Taking derivative on both the sides w.r.t x we get
⇒ dy/dx = [(x²x³)(1) - (x + 6)(2x⁴ + 3x²)] / (x²x³)²
⇒ dy/dx = -x⁴ - 12x² - 36 / (x⁶)²
At x = 0 we get y = ∞
Let's consider y(x²)(x³) = x + 6
When the curve intersects the y-axis, x = 0. However, this results in division by zero. Let's assume the equation was meant to be y(x²)(x³)=x+6. Then at x = 0, y is undefined. Let's instead consider y = (x+6)/(x⁵) Then at x=0, y is undefined. Let's assume there's a typo in the problem statement and that the intended equation is y = x + 6/(x⁵). This is also problematic at x=0.
Let's assume the question meant y = (x+6)/(x^5). Then at x = 0 the curve intersects the y-axis, and y is undefined. There must be a mistake in the problem statement.
Let's assume instead the equation is y = (x+6)/(x²+x³).
Then when x=0, y is undefined. There must be an error in the question. We cannot proceed without a correctly stated equation.
If we assume the equation is y = x + 6, then dy/dx = 1. The normal has slope -1. The equation of the normal at (0,6) is y-6 = -x, or y = -x+6. The point (12, -6) is on this line, but this point isn't an option. There is an error in the problem statement or the options.