Never ever ever cram multiple values into a single database field by combining them with some sort of delimiter, like a comma, or fixed length substrings. In the rare cases where this clearly gives a benefit in storage requirements or performance ... see rule #1: never ever ever. Ever.
When you cram multiple values into a single field, you sabatague all the clever features built into the database engine to help you retrieve and manipulate values.
Like let's say you have this -- I guess it's some sort of student database.
Plan A
student (student_id, account_id, class_id_mash)
Plan B
student (student_id, account_id)
student_class (student_id, class_id)
Okay, lets' say you want a list of all the students taking class #27. With Plan B you write
select student_id
from student join student_class on student.student_id=student_class.student_id
where class_id=27
Easy.
How would you do it with Plan A? You might think
select student_id
from student
where class_id_mash like '%27%'
But that will not only find all students in class 27, but also all those in class 127 or 272.
Okay, how about:
select student_id
from student
where class_id_mash like '%,27,%'
There, now we won't find 127 or 272! But, oops, we also won't find it if the 27 happens to be the first or last one in the list, because then there aren't commas on both sides.
So okay, maybe we could get around that with more rules about delimiters or with a more complex matching expression. But it would be unnecessariliy complex and painful.
And even if we did it, every search for class id has to be a full-fill sequential search. With one value per field and multiple records, you can create an index on the class_id field for fast, efficient retrieval. (Some database engines have ways to index into the middle of text fields, but again, why get into complicated solutions when there's an easy solution?)
How do we validate the class_id's? With separate fields, we can say "class_id references class" and the database engine will insure that we don't enter an illegal value. With the mash, no such free validation.