Initial value of time function
Initial Value theorem States that the initial value is given by:

$$
  \lim_{s \rightarrow \infty} sF(s)
$$

so in our case, the initial value, \$f_0\$, is:

$$
 f_0 = \lim_{s \rightarrow \infty}\frac{10s(s+6)}{(s+2)(s+3)} 
$$

$$
  f_0 = \frac{10s^2}{s^2} = 10
$$