How many diapers should a newborn baby go through in 6th months?

That's hard to say. There are many variables to this question, such as your child's potty habits: how many times a day does she pee/poop her diet, if she gets sick and has diarrhea, if she gets constipated...etc.

Ideally babies should be changed every 3-4 hours, and have around 12-14 waking hours, so if you figure about 4-7 diapers a day times 182.5 (half a year) you get 730-1,278 diapers every six months.

If you buy Pampers 84 packs for $20 (the brand/price I use) then you're looking to spend around $305 approximately.