I have seen this sentence translated as both "Only the Goddess knows fate" and "Only the Goddess knows their fate". That aside, I remember someone telling me that this was not correct Latin, and it has been bugging me ever since. What I have been able to piece together so far:
"sola dea" I am not sure about. I know that "dea" is a first-declension feminine noun in the nominative case. However, since "dea" is the active noun in the sentence, the one doing the "knowing", I am not sure that it should be in the nominative case. None of the other cases seem like they fit, except for possibly the accusative case, making it "solam deam".
"fatum" is a second-declension neuter noun in the accusative case, which I believe is correct, but I can't explain why. Something to do with it being the object acted upon.
Then the verb, "novit", infinitive form "noscere"? Or is it "nosco"? From this chart it looks like novit is in the perfect tense, which doesn't make any sense; would that not translate as "Only the Goddess has known fate"? This is the one I've been having the most trouble with and have been unable to figure out.