Hartke's owners manual said:
"When two speakers are wired in Parallel the total impedence is cut in half
FYI the bit above
only applies when both speakers have the same impedance rating. When they have different ratings, like a 4 and an 8 together, the math gets more complex.
But yes, running an 8 and a 4 in series will get you 12 ohms, and 12 ohms is safe. Unfortunately at 12 ohms your amp will only put out a small fraction of its potential power, IOW you'll get a
lot less watts from it if you do that.
Biamping is where the signal gets split (usually at the preamp stage) into two frequency ranges on two separate channels (lows and highs) and sent into two separate power amp sections. Typically the highs will go to a smaller (less watts) amp section. Each of those power amp sections will drive a separate speaker cab.
In the case of some systems that are designed for biamping, you can buy a "single cabinet" that is actually two separate systems in one big box. So with a head that is designed for biamping, the "highs" output on the amp would go to the highs input on the cab, and same for the "lows" output and inputs.
Or you could use separate cabs, like one big one for the low channel and one small one for the highs. You cannot biamp into just one input of one speaker cab.
I'm not sure about how the Hartke head handles those ohm loads coming out of two separate power amp sections; it may be that it will treat each cab as a completely separate load, i.e. not parallel
or series, in which case maybe the 4 and the 8 can work together. You'll seriously have to read the amp's manual carefully, and maybe even call Hartke, to answer that one for sure. The more I think about it, the more that would make sense;
IF I'm right, the, the biamped system (with two cabs) would
definitely be louder than the mono system with only one cab.