Key idea. Pair the outside numbers and the inside numbers.

1. Let \(u=2020\cdot2026\). The middle product differs from it by 8, because

   \[\begin{aligned}(2020+2)(2020+4)&=2020^2+6\cdot2020+8,\\2020(2020+6)&=2020^2+6\cdot2020.\end{aligned}\]

2. Therefore \(2022\cdot2024=u+8\), and the whole expression becomes \(u(u+8)+16\).

3. Now complete the square:

   \[u(u+8)+16=u^2+8u+16=(u+4)^2.\]

4. Since \(u+4=2020\cdot2026+4=4\,092\,524\), we have even found its integer square root.

Remember. Large numbers can hide a short identity. Compare the products before multiplying everything.