Ed had 12 more marbles than Doug. Doug lost some of his marbles at the playground. Now Ed has 32 more marbles than doug. How many marbles did Doug lose?
Ed had 12 more marbles than Doug. This means that if we start with Doug's number of marbles, then add 12, we will get Ed's number of marbles. So: 

Doug's number of marbles + 12 = Ed's number of marbles

Doug lost some of his marbles at the playground. This means that Doug's current number of marbles is less than what it was before. So: 

Doug's current number of marbles < Doug's number of marbles + 12

Now Ed has 32 more marbles than Doug. This means that if we start with Doug's current number of marbles, then add 32, we will get Ed's number of marbles. So: 

Doug's current number of marbles + 32 = Ed's number of marbles

We can solve this system of equations to find out how many marbles Doug lost.