Use a FOR /L loop and set the start to 0, the step to 4 and the end to 1200 which is one more than the 1199 number sequences of file name parts which you need only to copy the fourth file.
This will iterate the numbers starting at 0 going from 0, 4, 8, .... 1196 counting by 4's and you can append the iterated value as a string concatenated within a portion of a file name along with a wildcard mask and use that with xcopy to copy each 4th file accordingly.
Batch Script
Note: This logic assumes the file names will always start with "file-2" and always end with the sequence numbers just before the dot before the extension png (i.e. <SeqNum>.png).
@ECHO ON
SET SrcDir=C:\folder\src
SET DestDir=C:\folder\dest
SET fNamePart=file-2
SET ext=png
FOR /L %%a IN (0, 4, 1200) DO (
ECHO F | XCOPY /Y /F "%SrcDir%\%fNamePart%*%%a.%ext%" "%DestDir%\"
)
PAUSE
EXIT
Further Resources
FOR /L
FOR /L %variable IN (start,step,end) DO command [command-parameters]
The set is a sequence of numbers from start to end, by step amount.
So (1,1,5) would generate the sequence 1 2 3 4 5 and (5,-1,1) would
generate the sequence (5 4 3 2 1)
XCOPY