6 ohm speakers with 4/8 ohm amplifier

Whichever sounds best, don't worry, you won't hurt anything.

8 ohm may be fuller 4 ohm may be a little lean

try both it's fun!

I think the correct answer depends on the impedance curve of the speaker. 6 ohms is simply the nominal impedance. Without knowing the particulars of your speaker, I would say that the 4 ohm taps are the better choice, since the impedance will be lower than 8 ohms for much of the time.
As was said before, try both. It's possible you won't hear any difference. Only if the speaker's impedance drops into the 2 or 3 ohm range for a significant part of the audioband will the 4 ohm tap sound noticeably better.

For what it's worth I have revel performa30 with an arc vsi60 , base it tighter , Mids are cleaner on the 4 ohm tap. I wasn't happy with amp until I changed from 8 to 4 ohm

I have 6 ohm nominal KEF Q300 speakers and I use the 4 Ohm taps of my Jolida JD-502P amp. I found the bass to be slightly louder and tighter vs. the 8 ohm tap of the Jolida. I figure the KEF Q300s may dip below 6 Ohms so I might as well play it safe and use the 4 Ohm tap just in case.

Say your speakers are 6 ohms and your amp gives out 120wpc in 6 ohms.
So, if I am shopping for an amp for my 6 ohms speakers and care about the amp’s power rating, I should go by it is power rating at 6 ohms, correct?

I should also mention that I am just asking a technical question, not what I need/want as power or not.

It's about damping factor. The 4 ohm tap will increase the damping factor, most speakers are designed for this, better control over the woofer. However, you may not like it so as suggested try them both and see what you prefer.

Like it was suggested in the first post try both and let your ears decide which is the better of the two. No harm to your amp.

Maybe I should ask differently.

If a speaker manufacturer has the following specs; do they mean the recommended power in 8 ohms or 6 ohms?

Specs:
Impedance: 6 ohms
Recommended power: Minimum 50wpc