Okay, start simple. Basically, what you're struggling with is the concept that whatever you do to the bottom, you have to do to the top. Otherwise, you're making a different fraction - by following this rule, the fraction still equals the same thing.
Take 1/2
If you multiply the bottom by 2, then you get 1/4. This isn't the same as a half (obviously) BUT if you do the same to the top, and multiply by 2, then you get 2/4 which is the same as a half.
All you are trying to do in this question is change the fractions into a form that you can use.
The numbers don't have a relationship with 6. You are just applying the rule that WHATEVER YOU DO TO THE BOTTOM, YOU HAVE TO DO TO THE TOP