$ X(\omega)=\int_{-\infty}^{\infty}x(t)e^{-j\omega t}dt $
$ x(t)=te^{-6t-6}u(t-6)\,\ $
$ X(\omega)=\int_{-\infty}^{\infty}t^2 u(t-1) e^{-j\omega t}dt \; = \int_{1}^{\infty}t^2 e^{-j\omega t}dt $
