Kelly paid 176.56 Mike paid 942.57 for a total of 1119.13 Mike is paying for 2/3 of this what is the total that Kelly owes Mike

Are you sure this is the exact problem?

Mike is paying for 2/3rds of "this"? What is "this"? The total of $1119.13 or something else.

Work out the amount that Mike paid.

Then work out the amount that Mike paid for Kelly based on your previous answer and the total amount Mike has paid at the beginning. That is the amount that Kelly will owe to Mike.