Variable $x$ cannot be equal to $-2$ since division by zero is not defined. Multiply both sides of the equation by $2\left(x+2\right)$, the least common multiple of $x+2,2$.
$$2\left(x+1\right)=3\left(x+2\right)$$
Use the distributive property to multiply $2$ by $x+1$.
$$2x+2=3\left(x+2\right)$$
Use the distributive property to multiply $3$ by $x+2$.