Remove duplicates keeping entry with largest absolute value

First. Sort in the order putting the less desired items last within id groups

 aa <- a[order(a$id, -abs(a$value) ), ] #sort by id and reverse of abs(value)

Then: Remove items after the first within id groups

 aa[ !duplicated(aa$id), ]              # take the first row within each id
  id value
2  1     2
4  2    -4
5  3    -5
6  4     6