One thing that always puzzled me was why some terms and names that are based on numbers will mix the on and kun readings. I never really understood the rules for that, but it occurs to me that there must be some.
For example, the word yakuza is derived from 8-9-3, a no-score hand in the 花札 (hanafuda) card game. This comprises:
や — 8, ya(ttsu), a kun reading
く — 9, ku, an on reading
ざ — 3, za (for san), an on reading
Similarly, the famous Admiral Yamamoto had a given name of Isoroku (meaning, curiously, "56"), which mixed kun readings (or their variants) for 5 and 10 plus the on reading for 6.
I just want to know how to make sense of this — or if it is even necessary that it make sense. Perhaps it is simply a matter of putting together sounds that the originator(s) of the term found pleasing?
Edit: I want to add that the usages sometimes seem capricious to me, as when you hear 二人（ふたり）to refer to two people but 二人前（ににんまえ）to refer to a restaurant serving for two people or the task that two people have before them, although you can hear ふたりまえ there as well.