The 4 string arpeggio is mainly used for the D chord and also any variation on that D chord such as minor, major, seventh and so on. You could also use this arpeggio pattern over an E chord or any E shaped bar chord as the root note for those chords is also found on the 4th string as well as the 6th.
As with the other two arpeggios, root 5 & root 6, the pattern order is basically the same, it's just the first note that changes. This pattern is identical to the 5 string arpeggio although everything is just moved down one string. Once you get a feel for this arpeggio pattern order it will all flow from one chord to the next.
This is not the only arpeggio pattern we can play. If you want you can swap around the order of the notes and start creating your own patterns.
e|-------------X-----------|
B|-------X--------X-----X--|
G|----X-----X--------X-----|
D|-X-----------------------|
A|-------------------------|
E|-------------------------|
Chords to be used on
D & all variations (Major, Minor, 7th, etc.)
|-------------2-----------|
|-------3--------3-----3--|
|----2-----2--------2-----|
|-0-----------------------|
|-------------------------|
|-------------------------|
NOTE: sharp and flat chords will generally be taken from one of the 5 open chord shapes you have already learnt. For example the E shaped F# chord in only 1 fret higher than an F chord which is found on the 1st fret. The shape hasn't changed just the position, therefore you will still use the 6 string arpeggio pattern for both chords.