From $2x = 20$: $x = 10$.

From $3y = 20$: $y = \dfrac{20}{3}$.

From $4z = 20$: $z = 5$.

Now compute $12xyz$:

$12 \times 10 \times \dfrac{20}{3} \times 5 = 12 \times \dfrac{1000}{3} = \dfrac{12000}{3} = 4{,}000$