Which of these number(s) below are potential roots of the function p(x)=x^4+22x^2-16x-12

There's no list so we'll generate our own. Technically we're after zeros of p(x), which are the roots of p(x)=0.

The rational zeros are always fractions with a factor of the constant in the numerator and of the leading term in the denominator. Here we have a monic polynomial, leading coefficient 1, so the rational roots are all integers, factors of -12.

The potential rational zeros are: -12, -6, -3, -2, -1, 1, 2, 3, 6, 12