Move everything to the right...to the right in FCPX

Put your playhead on the cut before the first one of the clips you want to move to the right and press ALT + W. This will insert a gap just before the first clip.

Now you can drag the right edge of the gap clip to move everything behind it to the right (see screenshot 1)

Or you can select the gap clip, press CTRL+D and enter a duration in the timecode HUD. This will move everything behind it to the right with the exact duration you have set (see screenshot 2)

Best wishes,

Ronny