Answer: HANG and LEAN.
The remaining 8 words can be changed as follows:
HARD >> CARD, HERD, HAND, HARP
PORT >> FORT, PART, POET, PORE
DUCK >> MUCK, DECK, DUSK, DUCT
BAIL >> HAIL, BOIL, BAWL, BAIT
MAST >> CAST, MOST, MALT, MASK
THIN >> SHIN, TWIN, THAN, THIS
FIRE >> HIRE, FARE, FIVE, FIRM
READ >> BEAD, ROAD, REED, REAL
You have to be able to change EVERY letter to make a new word, so from HANG you can change H to make SANG, the A to make HUNG, and the G to make HAND, but you can't change the N to make a new word.