Step 1: Sort the four minerals by crystal system first, that narrows the space group fast.
Diamond is cubic. Graphite, despite also being pure carbon, is hexagonal because it is built of stacked sheets. Coesite, a dense silica polymorph, is monoclinic. Calcite is trigonal (rhombohedral).
Step 2: Attach the matching space group to each system.
A cubic, face centred, diamond type structure carries the label $Fd\bar{3}m$, so diamond (P) goes with option 3. A hexagonal close packed style layered structure carries $P6_3/mmc$, so graphite (R) goes with option 1. A monoclinic structure of this kind carries $C2/c$, so coesite (Q) goes with option 4. A trigonal rhombohedral carbonate carries $R\bar{3}c$, so calcite (S) goes with option 2.
Step 3: Collect the full match.
This gives P-3, Q-4, R-1, S-2.
Step 4: Compare with the four choices.
Option A puts diamond with $R\bar{3}c$ instead of $Fd\bar{3}m$, wrong. Option B puts diamond with the graphite space group, wrong. Option D shifts every pair away from what we found. Only option C, P-3; Q-4; R-1; S-2, lines up with our system by system match.
Step 5: Conclude.
\[ \boxed{P\text{-}3;\ Q\text{-}4;\ R\text{-}1;\ S\text{-}2} \]