Variable $m$ cannot be equal to $-\frac{3}{2}$ since division by zero is not defined. Multiply both sides of the equation by $3\left(2m+3\right)$, the least common multiple of $2m+3,3$.
$$3\left(6m-2\right)=4\left(2m+3\right)$$
Use the distributive property to multiply $3$ by $6m-2$.
$$18m-6=4\left(2m+3\right)$$
Use the distributive property to multiply $4$ by $2m+3$.
$$18m-6=8m+12$$
Subtract $8m$ from both sides.
$$18m-6-8m=12$$
Combine $18m$ and $-8m$ to get $10m$.
$$10m-6=12$$
Add $6$ to both sides.
$$10m=12+6$$
Add $12$ and $6$ to get $18$.
$$10m=18$$
Divide both sides by $10$.
$$m=\frac{18}{10}$$
Reduce the fraction $\frac{18}{10}$ to lowest terms by extracting and canceling out $2$.
