1. Principle used

A salt gives a basic solution in water if it is formed from:

• a strong base + weak acid r basic salt, or
• if one of its ions undergoes hydrolysis to produce $OH^-$ strongly.

A salt gives an acidic solution if it is formed from:

• a strong acid + weak base, or
• a highly charged metal cation hydrolyses water to produce $H^+$.

We examine each option.

2. Option A: $Pb(CH_3COO)_2$

This salt contains:

• $Pb^{2+}$ : cation of the weak base $Pb(OH)_2$-type metal hydroxide; metal cations like $Pb^{2+}$ undergo hydrolysis and tend to make solution acidic.
• $CH_3COO^-$ : conjugate base of weak acid $CH_3COOH$; this tends to make solution basic.

So both ions hydrolyse in opposite directions. However, $Pb^{2+}$ is a fairly polarizing metal ion and hydrolysis of the cation is significant. Hence this salt is not strongly basic.

3. Option B: $Al(CN)_3$

This salt contains:

• $Al^{3+}$ : very small, highly charged cation; it hydrolyses strongly and makes solution acidic.
• $CN^-$ : conjugate base of weak acid HCN, so it makes solution basic.

Now compare strengths:

• $Al^{3+}$ hydrolysis is very strong.
• Though $CN^-$ is basic, the strong acidic hydrolysis of $Al^{3+}$ dominates.

Therefore, aqueous solution of $Al(CN)_3$ is not the most basic; in fact it tends toward acidity due to strong hydrolysis of $Al^{3+}$.

4. Option C: $CH_3COOK$

This salt is formed from:

• $KOH$ = strong base
• $CH_3COOH$ = weak acid

Thus:

• $K^+$ does not hydrolyse.
• $CH_3COO^-$ hydrolyses as: $CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-$

So the solution is definitely basic.

Since there is no acidic cation present, the basicity is not opposed by cation hydrolysis.

5. Option D: $FeCl_3$

This salt is formed from:

• $Fe(OH)_3$-type weak base cation $Fe^{3+}$
• strong acid $HCl$

$Fe^{3+}$ hydrolyses strongly: $[Fe(H_2O)_6]^{3+} \rightleftharpoons [Fe(H_2O)_5OH]^{2+} + H^+$

Hence solution is acidic, not basic.

6. Final comparison

• $Pb(CH_3COO)_2$ : mixed hydrolysis, not strongly basic
• $Al(CN)_3$ : strongly hydrolysing acidic cation present
• $CH_3COOK$ : salt of weak acid and strong base, clearly basic
• $FeCl_3$ : acidic

Therefore, the most basic salt in aqueous solution is: $\boxed{CH_3COOK}$

So the correct option is C.