The polynomial functions \(p, r,\) and \(s\) are defined above. Which of the following is equivalent to \(3p(t)-2r(t)-4s(t) \) ?

$$ 3p(t)-2r(t)-4s(t) $$ $$ =3(2t+3)-2(t^2+1)-4(2t^2-5) $$ $$ =6t+9-2t^2-2-8t^2+20$$ $$ =\boxed{-10t^2+6t+27} $$

We can try substituting an arbitrary value of \(t\). For example, substituting \(t=0\):

Browsing the answer choices, only the last option evaluates to \(27\) when \(t=0\).