Effectively what you're asking is to solve this equation
x^2 - 12x + 48 = 0
Compare that to this form
ax^2 + bx + c = 0
to find that
Let's compute the discriminant (aka the stuff under the square root in the quadratic formula).
d = b^2 - 4ac
d = (-12)^2 - 4(1)(48)
d = 144 - 192
d = -48
The discriminant is negative, which tells us that there aren't any real numbered solutions to x^2 - 12x + 48 = 0
Therefore, we have no way to factor x^2 - 12x + 48 over the real numbers. Going back at the problem at hand: there aren't any real numbers that (a) multiply to 48 and (b) add to -12.
The two mystery numbers would be complex numbers in the form a+bi, where i = sqrt(-1). If your teacher hasn't covered these types of numbers yet, then you simply would say "no solution".