Ed had 6 more marbles than Doug. Doug lost some of his marbles at the playground. Now Ed has 14 more marbles than doug. How many marbles did Doug lose?
Ed had 6 more marbles than Doug. 

That means that if we start with Doug's number of marbles, then add 6, we'll get Ed's number of marbles. So: 

Doug's number of marbles + 6 = Ed's number of marbles

Doug lost some of his marbles at the playground. 

That means that Doug's current number of marbles is less than it was before. So: 

Doug's current number of marbles < Doug's number of marbles + 6

Now Ed has 14 more marbles than Doug. 

That means that if we start with Doug's current number of marbles, then add 14, we'll get Ed's number of marbles. So: 

Doug's current number of marbles + 14 = Ed's number of marbles

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

Doug's number of marbles + 6 = Ed's number of marbles
Doug's current number of marbles + 14 = Ed's number of marbles

Doug's number of marbles + 6 = Doug's current number of marbles + 14