20. Let $a, b, c$ be real numbers such that
$$
3 a b+2=6 b, \quad 3 b c+2=5 c, \quad 3 c a+2=4 a .
$$

Suppose the only possible values for the product $a b c$ are $r / s$ and $t / u$, where $r / s$ and $t / u$ are both fractions in lowest terms. Find $r+s+t+u$.