已知 $a\in R$，函数 $f\left(x\right)=\left\{\begin{array}{c}{x}^2-4,x>2\\ \left|x-3\right|+a,x\le 2,\end{array}\right.$若 $f\left[f\left(\sqrt{6}\right)\right]=3$，则 $a=$___________.