Hello and welcome!
Please make yourself at home and talk about your favorite old anime and manga. If you know what rec.arts.anime was, you'll feel right at home.
If you're up for it, reply here with a brief introduction including early anime memories and where you are today.
It was a Radio Shack 300 baud modem. A little googling seems to indicate is would likely have been a Tandy DCM-3 “Direct Connect” (as opposed to acoustic coupler) modem.
It was in-line between the wall and a phone so you would pick up the phone, dial the number, head the modem tone, press a red button on the top of the modem and hang up the phone.