Connect Kemper to active monitor and FOH

Hi and welcome.

I would send main outs to FOH set to stereo if connecting both, master mono if only connecting 1. Then for your ASM-12 id come out of the monitor out of the KPA to the ASM-12 then you can change the volume of the ASM-12 with the KPA and not effect the FOH. Hold the output soft button down and you will see you can change both volumes independently.

For recording I use the monitor out of the KPA as it is mono and I always record guitars in mono and I don't have to worry to change what the output is set on

no problem, let us know how you get on

Seconded the tip. The monitor out is designed for personal monitoring (thus the name), whether that's an active cab, a power amp + a cab, the FX return on a head, a personal wireless in-ear mix (not wired headphones, that's what the front jack is for), whatever. The Kemper's designed under the premise that you'll be going to some sort of mixer - a PA, recording console, home studio interface, whatever - and these are typically called the Mains, so your main out should go to the mains.

Alternatively, you could use the mains XLRs for connecting to the house/PA/console/whatever, and use a 1/4" out of the mains into the cab. You lose the front volume control and independent output EQ settings, but it's certainly doable, especially with an FRFR cab like the ASM. I did it this way running a power amp in stereo for a while. It worked fine, but it ended up being more of a hassle than anything. You would also have to lock it into mono mode since you're only running one speaker, which may or may not be an issue for you.

It's tricky, but I've done it. You have two options for output, considering you're using your mains for, well, the mains:

1. Connect up a 2 channel power amp (passive speakers) or 2 powered speakers to the left and right 1/4" mains (assuming you'd use the XLRs for the house snake/mixer). The downside of this is the front panel volume control needs to stay set (if set to adjust the main volume), or adjusting your mains volume via the volume knob will also adjust the volume sent to the house, and same with mains EQ. However, I believe the ASM-12 (which I think you said you're using) has their own volume controls - you'll need to use the volume control on it instead. Set the mains for what the house wants, and then you can adjust your stage volume on your ASM-12's, which sucks if you need to make minor tweaks. This would be semantically equal to daisy-chaining your Friedmans to send a mix to the house.
2. Connect up a 2 channel power amp (passive speakers) or 2 powered speakers to the direct out and the monitor output, and adjust your output settings so one is left, and the other is right. You can then tie your volume knob to control both of those outputs. This gives you the benefit of having separate house EQ/send volume that you can leave set, as well as separate volume/EQ for your monitors. The downside of this approach is if you adjust EQ for your direct out, you then need to make the same changes to your monitor out, as they aren't tied together. The other downside is this will not work if you're using the FX loop, as the direct output is used for the FX loop.

In either case, if you're playing a smaller gig, or a venue that doesn't do stereo that often (I've played my fair share), you can always flip to mono, though I'd also advise, in that case, only using one personal monitor, also set to mono. Your stereo field you hear on stage will be only used by yourself and could cause some weird phasing issues.

I've, personally, resorted to using a mono speaker for personal monitoring, and using the mains for just my feed to the board, whether mono or stereo. I've spent a lot of time trying to make it work and I was just never happy with a stereo rig on stage (for my personal monitoring, not the house), as the stereo field just got lost with all the other noise on the stage. But you may well be playing larger venues and have more capacity than I, and working with more professional sound engineers.