The key words are "Facharztausbildung" and "Studium an Fachhochschulen". The German university system has two different types of universities, "Fachhochschulen" (FH) with a slightly lower level, more oriented towards practical applications, and "Technische Hochschulen" (TH) and "Universitäten" more oriented towards abstract science and research. A "Facharzt" (http://de.wikipedia.org/wiki/Facharzt) needs an additional education beyond the university degree. I don't have the context for your quote, but my guess is that they are saying: "We can support (probably by a grant, i.e. money) studies at a (higher-level) university (that includes studies where the degree is Master or Doktor; for medicine-related studies it's nearly always a Doktor), but not at an FH; and we can't support the additional education needed for a Facharzt."

Humanmedizin = Medicine Zanmedizin = Dentistry Veterinärmedizin = veterinary medicine Facharztausbilding = doctoral training fördern = support Now you do the rest.