jmc

First, we use the distributive property to expand the first two factors:

$$\begin{array}{rl}3(x+4)(x+5)& =(3\cdot x+3\cdot 4)(x+5)\\ & =(3x+12)(x+5)\end{array}$$We use the distributive property again by adding the product of $3x+12$ and $x$ to the product of $3x+12$ and 5:

$$\begin{array}{rl}(3x+12)(x+5)& =(3x+12)\cdot x+(3x+12)\cdot 5\\ & =x(3x+12)+5(3x+12)\end{array}$$We use the distributive property again and combine like terms:

$$\begin{array}{rl}x(3x+12)+5(3x+12)& =3x^2+12x+15x+60\\ & =\boxed{3x^2+27x+60}\end{array}$$