Q.Which of the following relations is correct for the degree of hydrolysis of ammonium acetate?

Salt hydrolysis is the reaction of a salt's cation, anion, or both with water -- effectively the reverse of the neutralisation that formed the salt -- and it determines whether a salt solution ends up acidic, basic or neutral.

Strong acid + strong base (e.g. $NaNO_3$): neither $Na^+$ (conjugate acid of strong $NaOH$) nor $NO_3^-$ (conjugate base of strong $HNO_3$) has any real tendency to react with water, so there is no hydrolysis and the solution stays neutral, pH = 7.

Strong base + weak acid, anionic hydrolysis (e.g. $CH_3COONa$): the anion $CH_3COO^-$ (conjugate base of weak $CH_3COOH$) pulls a proton from water, $CH_3COO^-+H_2O \rightleftharpoons CH_3COOH+OH^-$, so $[OH^-]>[H^+]$ and the solution is basic. The hydrolysis constant follows from multiplying this equilibrium by the acid's own $K_a$: $K_h\cdot K_a=K_w$, so $K_h=K_w/K_a$; with $K_h=h^2C$ (Ostwald-style), the resulting pH is $pH=7+\tfrac12pK_a+\tfrac12\log_{10}C$. …