"distinguish clearly" is correct and usable in written English.
You can use it when you want to emphasize that something needs to be distinguished or separated from something else. For example: "You need to distinguish clearly between your responsibilities as a staff member and the responsibilities of a manager."
It does not, however, distinguish clearly enough between complex carbohydrates (good) and refined ones (bad).
We need to distinguish clearly what might be a fruit of the kingdom from what runs counter to God's plan.
By peddling innuendo and failing to distinguish clearly the undeniable fact of selection from the contested agent of selection, Hooper has done the scientific community a disservice" (Coyne).
But Europe must nonetheless recognise the need to distinguish clearly between partners, competitors, and opponents and to formulate a more sophisticated and articulated policy towards Russia in particular.
Most historians today argue that, on balance, it was becoming increasingly difficult to distinguish clearly between the nobility and the bourgeoisie.
Not only are the four functions hard to distinguish clearly, but unless a different group operates each branch, there is nothing to prevent their acting in concert.
This is the ability of the instrument to distinguish clearly between two points whose angular separation is less than the smallest angle that the observer's eye can resolve.
As the historian Geoffrey Hosking argues in his book Russia: People and Empire, Russia's historical problem is that it has never been able to distinguish clearly enough between the nation and the empire.
Watson doesn't distinguish clearly, or at all, between the two, and so his book manages to feel at once breathless and long-winded — much too rushed in its parts and too diffuse as a whole.
They do not distinguish clearly between the "sacraments" and such acts as the blessing of water on Epiphany Day or the burial service or the service for the tonsuring of a monk that in the West are called sacramentalia.
But by failing to distinguish clearly between terrorism and acts of war, he plays into the hands of those who argue that since America has been indiscriminate in the past -- for example, in its bombing of civilians in Tokyo, Nagasaki and Hiroshima -- it is hypocritical for Americans to be shocked when indiscriminate means are used against them.
