The product of some negative number and 22 less than twice that number is 220220. find the number.

Let's start by transforming that statement. Let number = x

The product of some negative number and 22 less than twice that number is 220220
Product means sum, i.e. when they are added. So:
-x + 2x - 22 = 220220
(Note how I transformed those words into that expression ^)
Now we solve:

x - 22 = 220220
x = 220242

- Side note, sorry but I could be wrong. The product could mean when multiplied, in which case simplify '-x*(2x - 22) = 220220'