You don't say what type of Terk antenna it is. 

If it is a big round 'loop' antenna (a plastic round loop with a knob on it), it's for AM/MW only, and you sit the antenna to the side of the radio (usually the side where the tuner knob sits), or in front of the radio, or behind it. 

You then tune to the AM/MW station you want to hear, and then tune the antenna to boost the station's signal, using the knob on the antenna.

You don't need to connect that kind of antenna to your boom box with a connector cable because the antenna 'connects' to your radio's internal AM/MW antenna magnetically.

It it's an antenna designed for FM, I don't know much about those.

lol...that reminds me how i use to back mid 80s use a roof antenna to get the the best reception, i also used a terk antenna with a decibel gain...that overload it at times....i tried T wall mounted antennas...all for long distant FM receptions...at times it worked better sometimes it just gave it more static....it was a trial and error thing...but yeah like deliverance said...usually on the back of the radio it should have two terminals to attach the antenna onto with the specified ohm rating

In the 1980's I used a large spiral loop AM antenna with my Sanyo boombox, and was able to hear central Mexican stations from the Western U.S., and even a couple stations from across the Pacific.  Some of the boomboxes have pretty good MW / AM sections, and a loop can take advantage of this. 

For FM I mainly have used the whip only, and to hear something from farther away it was reposition the radio, or take it in the car to a higher location.