exception

    Couldn't match expected type ‘Int’ with actual type ‘a’
      ‘a’ is a rigid type variable bound by
          the type signature for
            splitWhen :: (a -> Bool) -> [a] -> ([a], [a])
          at src/Data/List/Extras.hs:27:14
    Relevant bindings include
      n :: a (bound at src/Data/List/Extras.hs:29:23)
      xs :: [a] (bound at src/Data/List/Extras.hs:28:13)
      p :: a -> Bool (bound at src/Data/List/Extras.hs:28:11)
      splitWhen :: (a -> Bool) -> [a] -> ([a], [a])
        (bound at src/Data/List/Extras.hs:28:1)
    In the first argument of ‘splitAt’, namely ‘n’
    In the expression: splitAt n xs

stuff.hs

import Data.List

splitWhen :: (a -> Bool) -> [a] -> ([a], [a])
splitWhen p xs = case find p xs of
                 Just n -> splitAt n xs
                 Nothing -> (xs, [])

You can diagnose the type error more interactively by leaving out the explicit type for splitWhen, and checking if it compiles. It turns out that it does; inspecting the working, inferred type with ghci shows:

splitWhen :: (Int -> Bool) -> [Int] -> ([Int], [Int])

This means that the a type is too general: something inside splitWhen must be constraining it to Int. Looking at the types of the functions called by splitWhen, the first argument of splitAt stands out:

find :: (a -> Bool) -> [a] -> Maybe a
splitAt :: Int -> [a] -> ([a], [a])

It must be an Int, which is being matched with the result of find, which in turn is matched with the input predicate and list.

Knowing this, the GHC error message should hopefully make a bit more sense. :)