\[\begin{array}{l}
AC = 12 - AB\\
Ap\,\,dung\,\,dinh\,\,ly\,\,ham\,\,so\,\,\cos \,\,ta\,co:\\
A{C^2} = A{B^2} + B{C^2} - 2AB.BC.\cos B\\
\Leftrightarrow {\left( {12 - AB} \right)^2} = A{B^2} + {8^2} - 2.AB.8.\cos 60\\
\Leftrightarrow 144 - 24AB + A{B^2} = A{B^2} + 64 - 8AB\\
\Leftrightarrow 16AB = 80\\
\Leftrightarrow AB = 5\,\,cm.\\
\Rightarrow AC = 12 - 5 = 7cm.
\end{array}\]