Determine the following numbers.

Two consecutive integers with half of the small equal to 4 more than one third of the larger.

My work:

Let the value of 1st integer be x(1/2)

Let the value of 2nd integer be x+1(1/3)+4

x(1/2) = x+1(1/3)+4

...Am I right so far? If so, I have no idea how to solve this?

Help appreciated. Word problems are very hard for me. Thank you.