Let's simplify things...
For my 10-AA NiMH pack (total output: 1.2v x 10 = 12 v), shown in OP, I will plug in a common 12v wall wart (adapter) but NO resistor. Just a direct mating.
Do not do this. It is contrary to the advice given in this thread and will not work well, if at all.
When fully charged, an Eneloop reaches about 1.47 V at the terminals, so 10 in series will reach 14.7 V. You will need a charging voltage higher than 15 V. A supply of 12 V will not do it.
To charge the set of 10 cells safely in series, get a supply of, say 24 V and arrange that the current when fully charged is about 100 mA. Therefore we can choose a series resistor like this:
R = (24 - 10 x 1.47) / 0.1 = 93 ohms.
You could choose 100 ohms to make it a round number.
Then when the batteries are empty (cell voltage 1.2 V), the charging current would be:
Imax = (24 - 10 x 1.2) / 100 = 120 mA
For faster charging you could probably go to a 50 ohm resistor, but not lower than that.