Concept:
Knowledge may be classified in different ways.
Important distinctions include:
\[
\text{Knowing that}
\]
\[
\text{Knowing how}
\]
\[
\text{A posteriori knowledge}
\]
\[
\text{Skepticism}
\]
Step 1: Match A.
The statement:
\[
\text{A blue litmus paper turns red in acid}
\]
is known through observation and experiment.
So, it is a posteriori knowledge.
\[
A \rightarrow IV
\]
Step 2: Match B.
Doing philosophical reasoning well is a skill.
It is an example of:
\[
\text{Knowing how}
\]
So:
\[
B \rightarrow I
\]
Step 3: Match C.
The statement:
\[
\text{I don't know anything}
\]
expresses doubt about knowledge.
So, it is related to skepticism.
\[
C \rightarrow II
\]
Step 4: Match D.
The statement:
\[
\text{I know that Banaras Hindu University is located at Varanasi}
\]
is propositional knowledge.
It is:
\[
\text{Knowing that}
\]
So:
\[
D \rightarrow III
\]
Step 5: Final matching.
The correct matching is:
\[
A-IV,\ B-I,\ C-II,\ D-III
\]
Hence:
\[
\boxed{\text{(D)}}
\]