To solve the multi-step linear inequality $9y + 2(y + 6) > 5y - 24$, start by distributing to simplify the left side, which generates $9y + 2y + 12 > 5y - 24$ and combines smoothly to $11y + 12 > 5y - 24$. Subtract $5y$ from both sides to responsibly collect the variables on the left, leading directly to $6y + 12 > -24$. By subtracting $12$ from both sides, the constants are gathered firmly on the right, resulting in $6y > -36$. Finally, divide both sides by $6$ to comprehensively isolate the variable. Because $6$ is positive, the inequality's direction is seamlessly preserved, outputting $y > -6$. The solution is then efficiently graphed on a number line using a left parenthesis at $-6$ with shading strictly to the right. Under interval notation, the solution is explicitly captured as $(-6, \infty)$.