$\text{Total number of letters in ''BANANA''} = 6$
$\text{Total number of 'A' in the word ''BANANA'' }= 3$
$\text{ Total number of 'N' in the word ''BANANA''}= 2$
$\text{Total distinguishable permutations of the letters ''BANANA'' }=\frac{6!}{3! 2!}=60$