Step 1: Identify lanthanoid with low \(3^{rd}\) ionisation enthalpy.
Gadolinium (Gd) has half-filled \(4f^7\) configuration after losing three electrons, which gives extra stability.
So,
\[
A \rightarrow Q.
\]
Step 2: Identify f-block element with given configuration.
Configuration \([Rn]5f^2 6d^2 7s^2\) corresponds to Thorium (Th).
So,
\[
B \rightarrow R.
\]
Step 3: Identify \(3d\)-series metal with colourless \(M^{3+}\).
Scandium (\(Sc^{3+}\)) has \(3d^0\) configuration, hence colourless.
So,
\[
C \rightarrow S.
\]
Step 4: Identify metal with highest atomisation enthalpy.
Vanadium (V) has strong metallic bonding due to maximum number of unpaired electrons in \(3d\)-series, leading to high atomisation enthalpy.
So,
\[
D \rightarrow P.
\]
Step 5: Write final matching.
\[
A = Q,\quad B = R,\quad C = S,\quad D = P.
\]
Step 6: Match with options.
This corresponds to option (A).
Step 7: Final conclusion.
\[
\boxed{A = Q,\ B = R,\ C = S,\ D = P}
\]