Yes, the DMhat should work with the DM6. If it doesn't, you might have a bad cable.
From the Alesis website:
This hi-hat control pedal give you traditional hi-hat feel for controlling open/closed sounds with virtually all e-percussion modules and devices including the DM6, DM5, Trigger|iO, PercPad, SamplePad, PerformancePadand ControlPad. It has a full-size, die-cast footboard for professional durability, a slim profile that fits perfectly next to double-bass pedals, and integrated spikes and velcro for holding its position on carpet. You can also use the DMHat Pedal as a bass drum trigger for modules that have switch inputs including the ControlPad and PerformancePad.