We start with the expression \( (3r^{3} - 12r^{2} - 63r - 45) + (3r + 6) \).
Step 2: Combine Like Terms
Next, we combine the like terms in the expression. The terms involving \( r^{3} \) and \( r^{2} \) remain unchanged, while we combine the linear terms \( -63r + 3r \) and the constant terms \( -45 + 6 \).
Step 3: Simplify the Expression
After combining the like terms, we simplify the expression to obtain \( 3r^{3} - 12r^{2} - 60r - 39 \).