${f##*/} uses Remove matching prefix pattern to expand variable f and remove all characters up to and including the last slash (/) character from the expansion. So if f contains /one/two/three/four the expansion will be four


${base%_*} uses Remove matching suffix pattern to expand variable base and remove all characters from the first underscore (_) to the end of the variable. So if base contains june_1234 the expansion will be june

base=${f##*/} base=${base%_*} This will temperately assign base as per first description and then use this to re-assign it as per the 2nd description. so if f=/one/two/three/a_b_c_123 base will become a_b_c and f will remain unchanged.

num=${f##*_} assign variable num to everything following the last underscore from variable f

(( num > max[$base] )) && max["$base"]=$num If interger comparison of num is greater than array max[$base] then assign max[$base] to num.