Explanation
Correct answer: D.
Choice D is the best answer. The convention being tested is punctuation use between two main clauses. In this choice, a colon is correctly used to mark the boundary between one main clause ("goats are notoriously indiscriminate") and another main clause ("they will devour all kinds of shrubs and weeds") and to introduce the following explanation of goats’ nondiscriminatory behavior when it comes to what they eat.
Why the other choices are wrong
Choice A
Choice A is incorrect because when coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction. Furthermore, the conjunction "and" fails to indicate that what follows is an explanation of goats’ nondiscriminatory behavior when it comes to their diets.
Choice B
Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to join two main clauses ("goats…indiscriminate" and "they…weeds").
Choice C
Choice C is incorrect because it results in a run-on sentence. The two main clauses ("goats…indiscriminate" and "they…weeds") are fused without punctuation and/or a conjunction.