Join data using group_concat
According to your desired result, you should group_concat workers group by department's name.




select d.name, group_concat(w.work_id) workers_id
from   department d
join   worker w
on     w.department_id = d.id
group by d.name;



name                            | workers_id
:------------------------------ | :---------
Academic Personnel              | 6,4       
Anthropology                    | 3         
Arts &amp; Lectures                 | 5,2,7     
Business and Financial Services | 1         
Computer Science                | 8         



dbfiddle here