Answer
$3x$.
Work Step by Step
List the prime factors of each term. Identify the factors common to all terms.
$3x^{4}=(3)\cdot[x]\cdot x\cdot x\cdot x$
$9x^{2}=(3)\cdot 3\cdot[x]\cdot x$
$12x=2\cdot 2\cdot(3)\cdot[x]$
GCF=$(3)\cdot[x]$, or $3x$.