I'll explain the auction to date in some detail, because you may not be used to these methods.
2D is about 2-8 HCP and shows (exactly) a 5-card weak two in a major. Virtually any hand in range will open, suit quality is not a constraint, the only thing that will stop this toy being used is if the hand is too good.
Over 2D partner could have:
- doubled to show 13-15 (semi-)balanced or various strong hands
- bid 2H/2S/2NT/3C/3D natural constructive
- bid 3H/3S/3NT natural and strong
- bid 4C/4D two suited clubs+linked major
- passed on all weak hands
- passed on a pure take-out double of one of the majors anything up to a decent 17-count
Responder's pass of 2D is either
- long diamonds, could be weak, but could have a decent hand that just thinks this is the best place to play (long diamonds, no 4-card majors);or
- any weak hand that doesn't care if 2D ends the auction (opener is not invited to compete in diamonds)
Your double is any hand without an obvious other bid that doesn't want to pass out 2D. Partner will treat it systemically as a take-out double of diamonds (so lebensohl applies e.g. a jump to 3M is natural invitational with 5, a cue is game forcing etc) but it is known that you may not be the traditional t/o double shape.
Partner's 4H suggests playing in 4H.
Now what, if anything. As a special favour I've told you in the poll what your potential bids would mean, and you are pretty confident about these.