I'm not sure if you want B12 to just return "Poor Hitter" or "Poor Hitter" plus
the batting average  (ditto for B13 and "Good Hitter"). The following formulas
return the label plus the batting average:

B12: =IF($A$10=0,"",IF($A$11/$A$10<=0.25,"Poor Hitter " &
TEXT($A$11/$A$10,".000"),""))

B13: =IF($A$10=0,"",IF($A$11/$A$10>0.25,"Good Hitter " &
TEXT($A$11/$A$10,".000"),""))

Or, you could do it all in one cell: =IF($A$10=0,"",IF($A$11/$A$10<=0.25,"Poor
Hitter "& TEXT($A$11/$A$10,".000"), "Good Hitter "& TEXT($A$11/$A$10,".000")))

You haven't shown us the formula  you are typing or told us the error you are
getting.

I am not sure what I am doing
At Bat12
Hits3
Poor Hitter<.250TRUE
Good Hitter>.250FALSE =(B11/B10>0.25)

I have different answer as well and they do not match.

3/12 is EXACTLY .25...
You're not telling Excel what to do if it is .25, just < or >
so, use <= if you expect .25 to be "Poor".