There are no direct trains from Hann. Münden; rail passengers approach Höxter via Hannover, which is a complicated and time-consuming affair (routing from Hannover to Gottingen to Ottbergen to Höxter). If taking a train is your only option, allow plenty of time, and note that there are only 3 to 4 trips daily.
From Hann. Muenden, follow B80 northwest to the junction with B83, which will take you north to B64 which continues north into Höxter.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.