can I just use zinnzer primer over the varnish on my new cheap cabinets they are only 6 months old or should I sand them first?

it depends a great deal on what the existing finish is. Some cabinets have conversion or two-part finishes and nothing sticks to them very well. It is most certainly not a "varnish" that you are familiar with.

If the finish is a lacquer, then BIN, a shellac-based primer, will adhere to it.