An organic compound (X) with molecular formula $$C_3H_6O$$ is not readily oxidised. On reduction it gives $$(C_3H_8O)(Y)$$ which reacts with HBr to give a bromide (Z) which is converted to Grignard reagent. This Grignard reagent on reaction with (X) followed by hydrolysis gives 2,3-dimethylbutan-2-ol. Compounds (X), (Y) and (Z) respectively are:

The molecular formula of compound $$(X)$$ is $$C_3H_6O$$. Such a formula can represent either an aldehyde or a ketone.

(i) Aldehydes are oxidised very easily, whereas ketones resist mild oxidising agents.
Given statement: $$(X)$$ “is not readily oxidised”.
Therefore $$(X)$$ must be a ketone.

The only ketone having the formula $$C_3H_6O$$ is propan-2-one (acetone):
$$CH_3COCH_3$$

Hence $$\boxed{X = CH_3COCH_3}$$.

(ii) When a ketone is reduced (NaBH4/LiAlH4) it gives a secondary alcohol.
Formula wise: $$C_3H_6O \xrightarrow[\text{reduction}]{[H]} C_3H_8O$$.

Reduction of acetone gives isopropyl alcohol (propan-2-ol):
$$CH_3COCH_3 \;\;{\xrightarrow{[H]}}\;\; CH_3CH(OH)CH_3$$

Therefore $$\boxed{Y = CH_3CH(OH)CH_3}$$.

(iii) Secondary alcohols react with $$HBr$$ via $$S_N1$$ to give the corresponding 2° bromides.
$$CH_3CH(OH)CH_3 + HBr \longrightarrow CH_3CH(Br)CH_3 + H_2O$$

Thus $$\boxed{Z = CH_3CH(Br)CH_3}$$.

(iv) Bromide $$(Z)$$ is treated with Mg in dry ether to form the Grignard reagent:
$$CH_3CH(Br)CH_3 + Mg \;\xrightarrow{\text{dry ether}}\; CH_3CH(MgBr)CH_3$$

(v) A Grignard reagent adds to the carbonyl carbon of a ketone; after hydrolysis a tertiary alcohol is formed.
General rule: $$R\!-\!MgBr + R'CO R'' \;\xrightarrow{\text{anh.\,ether}}\; R\!-\!C(OMgBr)(R')(R'') \xrightarrow{H_2O} R\!-\!C(OH)(R')(R'')$$

Here,
$$R = CH_3CH(CH_3)\;,$$ the isopropyl group from the Grignard reagent, and
$$R' = R'' = CH_3$$ from acetone.

Product after hydrolysis:
central carbon attached to $$OH$$, two $$CH_3$$ groups, and an $$CH(CH_3)_2$$ group $$\rightarrow$$ a six-carbon tertiary alcohol.

Draw the longest chain (four carbons) and locate the substituents:
CH3-C(OH)(CH3)-CH(CH3)-CH3

Naming this structure gives 2,3-dimethylbutan-2-ol, exactly as stated in the question. Therefore our chosen set $$X, Y, Z$$ is consistent with every step.

The set appears in Option B:
$$X = CH_3COCH_3,\;\; Y = CH_3CH(OH)CH_3,\;\; Z = CH_3CH(Br)CH_3.$$

Hence the correct answer is Option B.