Step 1
Given
The given expression is $L\{9+6t\}$
Apply Laplace transform formula $L\left\{k\right\}=\frac{k}{s}$ , where k = constant $L\left\{t\right\}=\frac{1}{{s}^{2}}$
Step 2
Calculation $L\{9+6t\}$
=$L\left\{9\right\}+L\left\{6t\right\}$ $=\frac{9}{s}+\frac{6}{{s}^{2}}$ $=\frac{9s+6}{{s}^{2}}$ $=\frac{3(3s+2)}{{s}^{2}}$
Hence, $L\{9+6t\}=\frac{3(3s+2)}{{s}^{2}}$