The two-wire system uses a single pair (two wires) for both the transmitted and received audio signal; either as a sort of audio half-duplex or by frequency-shifting one band so it does not interfere with the other. A four-wire system uses a pair for receive and a pair for transmit, four wires in all. By physically separating the two audio streams the crosstalk is greatly reduced and you can better optimise the line for lower distortion, lover noise and a flatter frequency response. You'd want these advantages, for example, in an audio line used for a broadcast feed but you'd do without them for a domestic telephone which typically uses just the two lines. A four-wire modem therefore is designed for driving a link over a four-wire circuit to the modem at the other end. You can, however get four-wire to two-wire converters if you need them but to be honest just buying another modem will be cheaper
