Number of permutation of n objects with n1 identical objects of type 1, n2 identical objects of type 2, ......and nk identical objects of type k is $\frac{n!}{n_{1}!n_{2}!....n_{k}!}$

Permutation of letter BANANA are $\frac{6!}{3!2!}= 60$

Distinguishable permutation means the letters won't be repeated. Here BANANA contains 6 letters in which N has been repeated twice and A has been repeated thrice. Hence number of distinguishable permutations = 6!/(3!2!) = 60