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I was looking in the rule book for this but could not find any special rule. It does not seem right to be able to potentially run farther than you move in difficult terrain but I cannot find a rule. Any help is appreciated.

Just another example of the quirky little details in 40k, I think. My group rolls for run distance, and then takes the difficult terrain test, but you cannot exceed the difficult terrain test result no matter what.

So, if you get lucky, and roll a 6 for run distance, but only roll a 4 for the terrain test, you can only move 4".

I always say we should just take the terrain test and be done, but my group is full of schlubs who think all that arbitrary rolling makes it more interesting. Alas

“Running movement is not slowed by difficult terrain but models running through dangerous terrain must test as normal. Units that Run in the Shooting phase cannot charge in the following Assault phase."

You roll one die and move that far.

Thanks