How does sorting a string in an array of strings and then sorting that array come out to be O(a*s(loga+logs))?

In the image you ask "why add?" Well, they are independent operations, one that sorts each of a strings the length of each is s, and that's O(a * s log s), and one that sorts the array of a strings, the length of each is s to count potential comparisons between each two strings, that's another O(a * s log a). Independent operations means "add". Adding gives O(a * s log s + a * s log a), which is what you got when you extract out the common factors.

Got stuck on the same example! Remember that optimally it takes nlogn time to sort an array of n characters. For the final sort if we assume that each string in the array is of length 1 then we're again just sorting a characters so we get the aloga term, however the worst case length of each string is s so you need to do aloga comparisons s times.