Define the function list->oos. Develop auxiliary functions as needed.

Solution A solution w/o auxiliaries:

(define (list->oos loos)
  (cond ;; [PT 2: for 4 cond clauses matching definition]
    [(empty? loos) (make-oos 0 0 0)] ;; [PT 1: for 0 0 0]
    [(symbol=? (first loos) 'on) ;; [PT 3: for one correct clause]
     (local ((define r (list->oos (rest loos))))
       (make-oos (+ (oos-on r) 1) (oos-steady r) (oos-off r)))]
    [(symbol=? (first loos) 'steady) 
     (local ((define r (list->oos (rest loos))))
       (make-oos (oos-on r) (+ (oos-steady r) 1) (oos-off r)))]
    [(symbol=? (first loos) 'off) 
     (local ((define r (list->oos (rest loos))))
       (make-oos (oos-on r) (oos-steady r) (+ (oos-off r) 1)))]))

or, this one, which is at least conceptually easier:

  (define (list->oos l) ;; [PT 1]
    (make-oos (count 'on l) (count 'steady l) (count 'off l)))
  
  ;; count : Symbol List-of-events -> Number [PT 1]
  ;; count how often x appears in l [PT 1]
  (define (count x l)
    (cond ;; [PT 1: 2 cond lines/questions]
      [(empty? l) 0]
      [else (cond ;; [PT 1: cond sub expression]
              [(symbol=? (first l) x) (+ 1 (count x (rest l)))]
              [else (count x (rest l))])]))
  
  ;; Examples/Tests [PT 1]
  (= (count 'on (list 'steady 'steady 'on 'off 'steady)) 1)

Translate your examples for list->oos into tests.

Solution

;; TESTS: [PT 2, each one correctly; 0 if not examples]
(equal? (list->oos empty) (make-oos 0 0 0))

(equal? (list->oos (list 'steady 'steady 'off 'on 'steady)) (make-oos 1 3 1))