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There is no direct connection between Mukacheve and Prague.
You can take a night train from Mukacheve to Vienna and then change to a train from Vienna to Prague.
Mukacheve 00.54 – Vienna 11.21 → Vienna 13.10 – Prague 17.07
Even cheaper option is taking a direct bus from Mukacheve to Košice and then change to a night train from Košice to Prague.
Mukacheve 15.00 – Košice 18.15 → Košice 21.22 – Prague 05.54 (next day)
Hotels in Mukacheve (Booking.com)
Hotels in Prague (Booking.com)