Math Help - Differential equation-Laplace Transform

1. Differential equation-Laplace Transform

we started the section on Laplace Transform this past Friday but after looking over my notes and the text I still do not have a clue.
here is an example from the book:
Find L^-1{3/S^4} = L^-1{(1/2)*(6/s^4) = (1/2)t^3
I don't understand where the 1/2 came from or where the 6 came from.
2. That is just basic algebra. Isn't $\frac{3}{s^{4}}$ the same as
$\frac{6}{2s^{4}}$?.
$\frac{\not{6}^{3}}{\not{2}^{1}s^{4}}=\frac{3}{s^{4 }}$