Step 1: Recall the quantum numbers of the six quarks. The down (d) quark belongs to the first generation, along with the up (u) quark.
Step 2: Quarks split into two charge families. Up-type quarks (u, c, t) carry \(+\tfrac{2}{3}e\); down-type quarks (d, s, b) carry \(-\tfrac{1}{3}e\). Hence the d-quark charge is \(-\tfrac{1}{3}e\).
Step 3: Strangeness is a flavour quantum number that is nonzero only for the strange quark, \(S=-1\) for the s-quark. The d-quark is not strange, so its strangeness is \(0\).
Step 4: Therefore the d-quark has charge \(-\tfrac{1}{3}e\) and strangeness \(0\), which is option (C).
\[\boxed{Q=-\tfrac{1}{3}e,\quad S=0}\]