We're wiring a J-355 Jacuzzi Hot Tub and the instructions said to use 6-3 wire for a 60 amp installation. We purchased Romex 6-3 wire, type NM-B, from a local box store to run through the basement from the electrical panel to the GFCI panel mounted on the outside of the house. Is this an acceptable wire or should we have used a THHN or THWN wire?
to run through the basement from the electrical panel to the GFCI panel mounted on the outside of the house.
You actually are not saying you intend to run the NM outside. If you run it through your basement studs and joists and up a wall and penetrate the wall into the back of the GFCI Panel. Then you should be able to run the NM as outlined in NEC 334.15 and 334.17. However if the NM is to run on the exterior of the building then it must be enclosed in PVC, sealtite or carflex, or you need to use some other approved type of conduit or cable installation (UF) as stated in other comments and answers.