Could someone pls help me wid this physics question?

Since you want the count rate due to the sample only, first subtract the background from the total. ( 838-18=820). A half-life of 6 hours means half the atoms decay in 6 hours so after six hours the 820 count would be cut in half (820/2=410). After six more hours half of this amount would have decayed (410/2=205) So at the end of 12 hours the count rate due to the sample alone would be 205. ( the total count rate would be 223 if your teacher happens to ask - 205 from the sample plus 18 background) Good Luck !!