To begin with, stop relying on FOIL; it only works for binomials, so if you don't know how to multiply general polynomials, then you get into situations like this.
Basically, to multiply two polynomials:
$\displaystyle \left(a_1+a_2+\dots+a_m\right)\left(b_1+b_2+\dots+ b_n\right)$
You first multiply $\displaystyle a_1$ by each $\displaystyle b$ term, then do the same with $\displaystyle a_2$, etc. and then add them all up. So for instance, $\displaystyle (x+2y+z)(-x+y-z)$ would be $\displaystyle [x\cdot (-x) + x\cdot y + x\cdot(-z)] + $$\displaystyle [2y\cdot(-x) + 2y\cdot y + 2y \cdot (-z)] + $$\displaystyle [z\cdot(-x) + z\cdot y + z\cdot(-z)] = -x^2 + 2y^2 - z^2 - xy - yz - 2xz$. If you're the kind of guy (like me) who needs to have an explanation of a formula in order to really understand and be able to use it, that follows from distributivity. (the fact that $\displaystyle a(b+c) = ab + ac$)
Back to your question: both parentheticals do have 2 numbers; the term $\displaystyle 2\sqrt6$ means 2
times the square root of 6, not plus. So in this case you technically could use FOIL (but make sure you know how to do polynomials with more terms as well!), so the answer is
$\displaystyle (4+2\sqrt6)(3-\sqrt6) = 4\cdot3 - 4\sqrt6 + 2\sqrt6 \cdot 3 - 2\sqrt6\cdot\sqrt6$
which you would then simplify.