Hi there,
Depends on what you mean by big numbers: Multiplications with a lot of zeros or just multiplications with some digits.
Starting by with a lot of zeros:
1) The obvious one: Taking the zeros out - doing the math - adding zeros in the end.
2) Working with letters instead of the actual zeros (i.e. client revenues are 100,000€ = 100k€) and knowing how they relate (i.e. k x k = M)
3) The most common mistake is for people to miss on the actual number of zeros - the easiest way to solve this problem is to (at the end) quickly round the numbers and see if makes sense (i.e. 12,433 x 1.78B = 22,130B lets say you instead of saying the correct number miss on a zero by mistake, just multiply 10,000 by 2B and you clearly see that it would be around 22,000 and never 2,200)
Regarding the second point with several digits
1) there are several ways to work it, trying to memorize multiplication tables, shortcuts - but for big ones I wouldnt worry much - from my experience with cases those are very rare, most of math is rather simple actually.
2) https://managementconsulted.com/mental-math-consulting/ This is a good tool for you to learn some quick ideas and to actually learn how to talk through your math which can be even better.
My 2cents