So your Stereo has a home and it might be the rumpus room (I like that term). The new speakers are lets say in the kitchen and the AppleTalk is there as well.

You have a cable from the Hi-Fi in the rumpus room to the central spot where the telephone connections are. You have a cable to each speaker if you want them several feet away from each other in the kitchen. The AppleTalk jack can be reached from one if not both of these locations in the kitchen or maybe a separate cable for this. All this said we can begin to modify the speaker connections.

At some home supply stores and electrical supply houses they have a 8 pin type of plug to snap on to solid 24 gauge wire. Get several of these to suit your needs. Use scraps from your project to reach the jack from the speaker and wire thusly:

Left speaker uses (from the chart above) the white green pair in the cable. If you are fluent with the configuration of the pins on the jack/plug wire ONLY these two conductors and label the plug LEFT. Do the same for the right speaker but use the white brown pair and of course label this RIGHT. If you are like me & have two sets of speakers that are the same models and try to tell which are right and left wired can be pesky to find in a hurry. The labels really help. Use the white green to the positive terminal of the left speaker. With the chart above connect the rest of the speaker terminals.

If you are not fluent with the 8 pin jack/plug arrangements carefully consider this:

Imagine you are looking at the jack from the front and the tab that locks the plug into the jack is downward. This would present the pins inside the jack horizontally. Looking from left to right the actual pins are numbered from 1 to 8 as in a RJ45 configuration. The centre pins for a regular telephone would be pins 4 & 5. The AppleTalk uses pins 3 & 6. See a pattern forming here? The next pins on either side of the AppleTalk pins are the Stereo left, and finally the outside pins are for the stereo right channel.

Speaking of RJ45, I must confess that it is not a RJ45 because if it was then only the centre 2 pins would be used. The registered jack (RJ) designation applies only to how the jack is wired, not how it looks. Example; you have a 4 pin jack on the wall and you cannot tell how it is wired. You plug in a phone and only line one works, this is wired as a RJ11 jack. If you had line one and two this would be a RJ14, or if it had only line one and A leads then it would be a RJ12. A RJ48 uses the first 2 pins and the last 2 (1,2,7 & 8) and now my head is hurting. If it was a 6 or 8 pin jack same deal, it only matters how the jack is wired , not necessarily the size of it or how many pins it has.

NOTE: DO NOT be too worried about the signal loss of the stereo from the Amp to Speaker. The amount of current and the voltage of the signal is nothing to worry about unless you have an exceptional sound system designed for exact specifications. To put your fears to rest next time you visit a stereo shop look inside the average amplifier and see how small the wire is inside the unit. You will have very little trouble even if you have a 100' run of cable. The specs for 24 gauge wire is about 50 ohms for 1000 feet and unless to plan to have your HiFi in the next town you will be able to sleep at nights. The wiring devices for telephone applications are designed for 2 amps and this is fine.
If you are one of those who push hundreds of watts of power to your audience, leave your present setup as is and add some pleasure to your kitchen or bathroom as far as that goes with an extra set of speakers. Something to consider for bathrooms, automotive speakers are the perfect things for bathrooms since they are designed for extremes of humidity. The stylish cabinet types are perfect and once in a while you can find them in colors. Imagine singing in the shower with the real tunes rather than trusting your memory. If you have the sound system that audio mags dream of, you can likely keep it down in the bathroom and kitchen. How would you hear the egg timer?