$\begin{align}  & f(x)=3{{x}^{2}}+x-f(1)\xrightarrow{x=1}f(1)=3{{(1)}^{2}}+1-f(1)\Rightarrow f(1)+f(1)=4 \\  & \Rightarrow 2f(1)=4\Rightarrow f(1)=\frac{4}{2}=2\Rightarrow f(x)=3{{x}^{2}}+x-2 \\  & f(0)=3{{(0)}^{2}}+0-2=-2\Rightarrow f(f(0))=f(-2)=3{{(-2)}^{2}}+(-2)-2 \\  & \Rightarrow f(f(0))=3(4)-2-2=12-4=8 \\  & f(1)=2\Rightarrow f(f(1))=f(2)=3{{(2)}^{2}}+2-2=12 \\  & \Rightarrow f(f(0))-f(f(1))=8-12=-4 \\ \end{align}$