Is it possible to charge 6 series Ni-MH cells using bq25703a or bq24780s?
What's confusing about TI stating this charger is for 1-4 cells?  It is not a 6 cell charger.  Just looking at the parametric data on their website for the BQ25703A, TI states its max battery voltage is 19.2V.  It shows it right in that chart, and probably warns you about it where you scribbled it out.  If you had six cells at 3.8V you're looking at 22.8V you would clearly be over the maximum battery voltage.  Worse if they float up when fully charged.  If you want to charge 6 cells look for a 6s charger.