To be divisible by 4,5, and 6, a number must be a
multiple of their least common multiple.  So we
find the least common multiple, LCM:

  4 = 2·2
  5 =       5
  6 =   2·3
------------------
LCM = 2·2·3·5 = 60

So each nmust be a multiple of

To find the first multiple of 60 greater than 200,
divide 200 by 60

     3 1/3
60)200
   180
    20

The next integer greater than  is 4, so
multiply 60×4 = 240, which is the first one, then
add 60 successively until you get the largest one
not exceeding 600: 

1. 240
2. 300
3. 360
4. 420
5. 480
6. 540
7. 600 ?

Note: You'll have ask your teacher whether to include
600 or not.  The word "inclusive" or "exclusive" to
tell whether 600 is considered "between 200 and 600" or not,
should have been given in the problem.

Edwin