The best thing to do is to multiply both sides by a number that is divisible by both 6 and 7. That number would be 6*7=42
so: 42* [x/6 - y/7] = 42* 1
Therefore: 7x - 6y = 42 (this is probably the most important step)
Now you can just rewrite this as: 6y = 7x - 42
finally divide both sides by 6: y = (7/6) x - 7
Let me know if you have any questions.