If black is allowed to castle then he must have just played g5 which allows 1. hxg6 threatening Rd8# and if 1. ... 0-0 then 2. h6#.
If black did not just play g5, then he just moved his king or rook which means he can't castle and white can play 1. Ke6 followed by 2. Rd8#.
Retrograde Analysis is a gerneof chess promblemes were the legality of the position is a key element. A position is legal if it can be reached through a legal chess game(no matter weird). Retros (i.e. promblems with Retrogade Analysis content)
may ask for e.g.amate in two, but the main content is in explaining the history of the position. Part of it anyway.
e.g.
... mate in 2!!