4 or 8 ohm connection for a 6 ohm speaker?

As most have said already, try the lower option first. I have a pair of speakers that average around 12 ohms during play. I tried the 8 ohm posts first and was disappointed. I the 4 ohm post and the speakers sounded much better. 

HI, 
Some tube amps behave better on 8ohm taps. As your speakers demand a little push the 4ohm tap would propably be better but you wouldn't know till you have tried.

Thanks for everyone's input! Much appreciated!

Originally I had placed the speakers on the 8 ohm taps as recommended by the person who sold the pair to me...he had a tube stereo power amp. After listening to my setup at home on my Dynaco MK 3's I was never really satisfied. Is it possible that the bass was less than satisfactory and the highs were shrill? I still enjoyed listening to the speakers though and I did try positioning them slightly differently but left it that way until now. 

Today I moved the speakers to the 4 ohm tap and listening to the same music the bass was way way more full and the highs were less shrill...is that possible? I feel that is what I heard (my hearing isn't what it used to be). I do honestly think the music is better on the 4 ohm tap and I am sure I heard distortion when on the 8 ohm tap. My audio source was from a Bluesound Node 2i playing music from Tidal. 

I feel definitely more satisfied now and nothing blew up LOL. 

Bill from Nova Scotia

As others have said, try it and see what you like best.  My experience is similar to yours.  I have Harbeth Super HL5 Plus and with some recordings, they sounded a little hot on the top end, or as you put it, "shrill".  I knew they shouldn't sound like that and switching to the 4 ohm taps on my Rogue M-180 monoblocks did the trick of taming that, while not losing any of the luscious mid-range.  I use four subwoofers, so wasn't looking to gain anything in the bass department, but I did end up turning the volume down a little on the subs after making the change.

Very interesting, that's exactly what I experienced. I am trying to listen again like I did when I was a teenager. I really like the midrange from the Thiel's as I really enjoy female voice and jazz. Listening to the beautiful soundtrack from Philip Glass "Tales from the Loop". 

On a side note, Harbeth and Rogue Audio equipment are definitely on my wish list...but I am very happy for the time being though with the budget I have.

Wishing you all a great Sunday and week ahead!

Bill from Nova Scotia