The purpose of this question is to strengthen your diagramming skills and familiarity with quantifiers (i.e. some v. most v. all), which is a form of reasoning that appears in the Logical Reasoning section.
If you haven't checked out our curriculum yet, I recommend viewing the 'Quantifiers' video in the Logical Reasoning portion of the curriculum. In the video, Mehran goes over why this form of notating some v. most v. all statements makes the most sense on the LSAT and allows you to answer quantifier questions as quickly as possible. Whether or not this is the correct way to write formal logic is another question. The goal of this notation is to help you arrive at the correct answer on the LSAT as efficiently as possible.
In the question we're looking at, we're given one of two premises and the conclusion, and we're tasked with figuring out what the second premise is that—when combined with the first premise—allows us to arrive at the given conclusion.
P: D-most-B
P: ?
C: B-some-C
The given premise can be re-written as B-some-D. Since the conclusion states B-some-C, how can we connect the given premise to the conclusion? We need to connect D and C in a manner that allows us to conclude B-some-C
P: B-some-D
C: B-some-C
If we add D - >C, then we can conclude B-some-C because adding D - >C to our chain would give us
B-some-D - >C
If at least one B is a D, and all Ds are Cs, then there has to be at least one B that's a C, which gives us our conclusion B-some-C
Hope this helps. Let us know if you have any more questions!