\(\left(x-4\right)\cdot2^{2020}=2^{2022}\)
\(\Rightarrow\left(x-4\right)\cdot2^{2020}-2^{2022}=0\)
\(\Rightarrow2^{2020}\cdot\left[\left(x-4\right)-2^2\right]=0\)
\(\Rightarrow2^{2020}\cdot\left(x-4-4\right)=0\)
\(\Rightarrow2^{2020}\cdot\left(x-8\right)=0\)
\(\Rightarrow x-8=0\)
\(\Rightarrow x=8\)