Thank you folks for weighing in. I think the logic I was presented with was something like: Racial hit dice give you feats; Levels give you feats; Therefore Racial hit dice count as levels. I thought it was pretty cut and dry that Character level=Class level, so when I was present...
I think the chance of getting 138 for instance is the chance of getting an adjusted result of 6 from each of 4 dice. The chance of that for each die is 2/3, so the overall chance is that to the power of 4 - or just under 20%. The chances given for other higher scores ...
You can also choose which hit dice to use when expending them during short rests. For example, if your PC is only slightly injured, you might use a d8 hit dice (from the bard side) to recover HP. Or, if your PC is badly injured, you might use all of their hit dice (the d8s ...