The easiest way to eliminate D-some-C is to remember a rule that applies to all categorical syllogisms, such as this problem. It is impossible to form a valid conclusion from two "particular" premises - a "particular" premise is a premise with a quantifier in it, whereas a universal premise is a premise that concerns the whole class of an object, e.g. all As are Bs. Since one of our premises here is particular -D -most-B, we know that the second premise must be universal, otherwise, there will be no valid conclusion.
To illustrate why this is the case, let's consider the following example:
Most birds (D) can fly (B). ? Some objects that fly (B) carry passengers (C)
If you say that the missing premise is D-some-C it translates into some birds carry passengers, which even if it is true, fails to show that there is any overlap between these two groups - birds that fly and birds that carry passengers, it is plausible that only birds that cannot fly,e.g. ostriches - carry passengers (true story!). Since we cannot conclude that there is any overlap between these two groups, we could not logically conclude that some objects that fly carry passengers.
Let me know if this makes sense and if you have any further questions.
