If I purchase a 6 unit property, and sell two of the units, could I then refinance into a FHA loan?

No

Much more info needed.. if the 6 units are all one one lot, and you have a loan against it, then no, probably not.. There so many things going on here that make this difficult that its impossible to advise you without looking at the complete existing loan and property details. Is there one loan or 6 loans? is there one parcel or 6 parcels? If they are all on one parcel and one loan, will the existing lender allow for a partial release? Are you living in one of the units? etc, etc, etc.. If you want to know for sure, you're going to have to find a local mortgage professional, pick up the phone and talk to someone so they can get all the details necessary to advise you properly.. I'm a Broker here in Scottsdale AZ and I only lend in Arizona. If you or someone you know is looking for financing options, feel free to contact me or pass along my information. William J. Acres, Lender411's number ONE lender in Arizona. 480-287-5714 WilliamAcres.com NMLS# 226347

The property (all structures on the same deed) securing the mortgage cannot include more than 4 units. Condo's have to financed separately, if that helps