north1mile writes:

My playing partner's hand consisted of a 10 & three 4s. The cut card was a 3. I thought this should be scored as a hand of eight points. He (and others) thought this should be scored as a hand of twelve points. So, just wondering, what is correct?

Look for the 15s first; the 10 can't make 15 with any combination of the other cards, and you need all of the others (4-4-4-3) to make one 15. So that's 2 points.

Now count pairs; three 4s gives you three pairs, for 6 points.

Runs and flushes there are none, and no points for nobs, so that makes 8 in all. You should ask your partner to explain where the remaining 4 points come from if he would like to claim them!