this is a sure-win endgame, there are many ways to win as long as red does not make any critical mistakes
the solution offered is the most direct and efficient

chariot (R) 2+1 king (k) 6+1
if on 3rd move red R2+1 black has elephant (e) 5+7 (if e5-7 then R2=3, k6=5, H3+4 red wins by capturing black's chariot) it may take a longer time for red to win although should still win the the end =)

example of another way to win is:
R2+1 k6+1
H3+4 e5-7
R2=5 r7+6
A5-4 r7=6
K5+1 r6-6
H6-4 r6=4
R5=3
Red wins by trading horse with chariot
But the original solution offered is more elegant

I'm writing this at my work place. I may have missed some moves so do let me know if there are any mistakes.