Here is a solution to count-short-strings:

;; count-short-strings:  list-of-string -> number
;; consumes a list of strings and produces the number
;; of strings in the list with fewer than 6 characters
(define (count-short-strings alos)
   (cond [(empty? alos) 0]
         [(cons? alos) (cond [(< (string-length (first alos)) 6)
                                 (+ 1 (count-short-strings (rest alos)))]
                             [else (count-short-strings (rest alos))])]))

An alternative way to write the function is like this:

;; count-short-strings:  list-of-string -> number
;; consumes a list of strings and produces the number
;; of strings in the list with fewer than 6 characters
(define (count-short-strings alos)
   (cond [(empty? alos) 0]
         [(cons? alos) (+ (cond [(< (string-length (first alos)) 6) 1]
                                [else 0])
                          (count-short-strings (rest alos))))]))