So what you have is binding posts (I assume) with a specified 75 Ω input. That's unusual, but let's run with it.
First of all, you can use a 75-300 Ω “matching transformer” that has the right ends, and it will probably work just fine (reception does not care very much about impedance mismatches), but it's not the way to get the absolute best performance.
Instead, what you want to do is to connect the 75 Ω cable directly with no transformer. You can make an adapter without needing to buy any specialized parts or solder anything:
Find a friend who's throwing out some coax, or ask a cable TV installer for scraps, or worst case go buy from the hardware store:
- a standard 75 Ω "F" connector coaxial cable, as short as you can find.
- a "F" coupler (as you would use to connect two cables).
Cut the cable, so you have a short piece with a connector on one end.
- Using a knife, wire stripper, or a coax stripping tool if you have one, carefully strip off the outermost insulation for an inch or so, revealing the braid (outer conductor).
Unbraid the braid, then bundle the fine wires off to one side (so that they are not surrounding the center conductor any more) and lightly twist them together like they were a piece of stranded wire, for later convenience.
Strip off the dielectric (insulation) around the center conductor, but not so far back it'll short against the shield.
- Use the coupler to attach this to the end of your antenna cable.
Connect the shield wire to the "GND" binding post and the center wire to the "FM ANT" binding post. Make sure no stray wires from the shield are shorting.
(Make sure they're not pulled down to short against each other by the weight of the coax — perhaps an adhesive cable clamp stuck onto the case over in the free space to the right would help as strain relief.)