To solve the inequality $8p + 3(p - 12) > 7p - 28$, first simplify each side by distributing to get $8p + 3p - 36 > 7p - 28$, which condenses to $11p - 36 > 7p - 28$. Next, collect the variables on the left side by subtracting $7p$ from both sides to obtain $4p - 36 > -28$. Add $36$ to both sides to collect the constants on the right, yielding $4p > 8$. Divide both sides by $4$. Since $4$ is notably positive, the inequality symbol remains exactly the same, culminating in $p > 2$. Graph the solution on the number line with a left parenthesis at $2$ and shading stretching to the right. In interval notation, the solution is written securely as $(2, \infty)$.