Making Suppositions

Let $c$ denote the number of chickens and $g$ the number of goats. The given information then translates into

$\begin{cases} c + g = 60 \\ 2c + 4g = 144 \end{cases}$ .

Dividing the second equation by $2$ and subtracting the first from it, we get

$\begin{cases} c + g = 60 \\ c + 2g = 72 \\ \end{cases} \Rightarrow g = 12$

and then

$c = \boxed{48}$ .