Dude ran to church to work out (6)
I believe the answer is:
deduce
'to work out' is the definition.
(to deduce is to work out or figure out)
'dude ran to church' is the wordplay.
'ran' indicates anagramming the letters (letters have run around).
'to church' becomes 'CE' (Church of England).
'dude' anagrammed gives 'dedu'.
'dedu'+'ce'='DEDUCE'
(Other definitions for deduce that I've seen before include "Infer like Sherlock" , "Arrive at conclusion from studying facts" , "Draw conclusion" , "Infer from the evidence" , "Reason through logic" .)