Concept:
The given equilibrium is
\[
[Co(H_2O)_6]^{2+}+4Cl^-
\rightleftharpoons
[CoCl_4]^{2-}+6H_2O.
\]
The forward reaction is stated to be endothermic.
According to Le Chatelier's principle,
• Increasing temperature favours the endothermic direction.
• Decreasing temperature favours the exothermic (reverse) direction.
Therefore, cooling shifts the equilibrium towards the pink hexaaquacobalt(II) complex.
Step 1: Identify the colours of the complexes.
\[
\boxed{
\begin{aligned}
[Co(H_2O)_6]^{2+} &\rightarrow \text{Pink}\\
[CoCl_4]^{2-} &\rightarrow \text{Blue}
\end{aligned}
}
\]
Step 2: Apply Le Chatelier's principle.
Since the forward reaction is endothermic,
\[
\boxed{\text{Cooling favours the reverse reaction}.}
\]
Hence, the equilibrium shifts towards
\[
[Co(H_2O)_6]^{2+}.
\]
Step 3: Predict the observed colour.
As more pink complex is formed,
the solution gradually changes from blue to
\[
\boxed{\text{Pink}.}
\]
Therefore,
\[
\boxed{\textbf{Option (D)}}
\]
is the correct answer.