I'm not a teacher, but "comprehensible" means simply "understandable", "able to be comprehended", as in "because of his excellent education, his English was quite easily comprehensible."
"Comprehensive" technically means something similar. Here is the OED's first entry under "comprehensive":
Characterized by comprehension; having the attribute of comprising or including much; of large content or scope.
The bit I've made blue is the meaning most commonly associated with "comprehensive". It is listed among the later entries in the OED as " Embracing many things, broad in mental grasp, sympathies, or the like."
So a "comprehensive education" is one that covers many subjects, that has a broad scope or range. Such a "comprehensive" education could make you "comprehensible" when talking on any of the subjects covered.
An extended use of this "broad, large content" meaning can be seen in the adverb "comprehensively", as in "today, the New Zealand cricket team was comprehensively beaten by England". Here "comprehensively" could be read as "thoroughly, completely, to a large degree".