"The man does not speak Greek."
Translation:Ο άντρας δε μιλάει Ελληνικά.
According to the current spelling rules (see e.g. http://ebooks.edu.gr/modules/ebook/show.php/DSDIM-F102/580/3784,16613/ ), δεν is used before κ π τ ψ ξ (mnemonic: κάποτε ψάξε "find sometimes"), their voiced equivalents μπ ντ γκ, as well as before vowels; δε before other consonants.
So δεν μιλάει is not correct according to these rules.
Unfortunately, it's not easy to correct the Greek sentence. But the current spelling is accepted in English-to-Greek exercises.