🚀 go-pugleaf

 It looks like you have a bi-amp system; that is, some stereos were designed
with separate amplifiers for the bass and treble ranges to get more power.
Try this: hook up one pair, then the other and see which is the bass and which
is treble.

 Now comes the fun. Since your new speakers do not have separate connections
to the woofer and the mid/tweeter sections, you may have to do minor 
surgery. If they are coaxials you will have to find the flexible braided
wires coming through the woofer cone, cut them where they come out the front
face, and solder them to a makeshift connector for the treble wire pair.
(easy with that axe, pilgrim!)

 If your new speakers are arranged with the woofers and mids/tweeters separate
on the speaker face, it will be a bit easier - same idea but less risk to the
woofer cone.

 The only other problem to worry about is whether the new speakers' tweeters
are able to stand whatever the amp is feeding them. Only one way to find that
out....