The increasing order of the acidity of the $$\alpha$$-hydrogen of the following compounds is:

For any carbonyl compound, the acidity of an $$\alpha$$-hydrogen depends on how well the conjugate base (the enolate ion) is stabilised. Two main factors decide this stabilisation:

(i)  Inductive (-I) effect of the carbonyl group.
(ii)  Resonance delocalisation of the negative charge after deprotonation.

More electron-withdrawing carbonyl groups and better delocalisation make the enolate ion more stable, so the parent carbonyl compound becomes a stronger acid.

The four compounds given in the question are:

(A) $$CH_3CHO$$          (acetaldehyde)
(B) $$CH_3COCH_2COCH_3$$   (pentane-2,4-dione; a $$\beta$$-diketone)
(C) $$CH_3COCH_3$$        (acetone, a ketone)
(D) $$CH_3COOCH_3$$       (methyl acetate, an ester)

Case 1 - Compound B (β-diketone)
After removal of an $$\alpha$$-H, the negative charge is delocalised over two carbonyl groups by resonance: $$\ce{-CH^-}$$ ⇌ $$\ce{-COCH=CO-}$$. This extensive delocalisation gives very high stability to the conjugate base. Hence B is the most acidic of the four (pKa ≈ 9-10).

Case 2 - Compound A (aldehyde)
In an aldehyde, the carbonyl carbon is bonded to only one electron-releasing alkyl group, so its -I effect is stronger than that of a ketone. The resulting enolate $$CH_3CH^-O$$ is therefore better stabilised than the ketone enolate. Aldehydes are thus more acidic than simple ketones (pKa ≈ 17).

Case 3 - Compound C (ketone)
A ketone has two electron-releasing alkyl groups attached to the carbonyl carbon. These reduce the overall -I effect, so the enolate ion is less stabilised than that from an aldehyde. Hence ketones are weaker acids than aldehydes (pKa ≈ 19-20).

Case 4 - Compound D (ester)
In an ester, the carbonyl is attached to an -OR group. Although the carbonyl itself has a -I effect, the -OR group can donate electron density to the carbonyl carbon by +R (mesomeric effect). This electron donation notably decreases the withdrawing ability of the carbonyl, making the ester enolate the least stabilised of the four. Consequently, esters have the least acidic $$\alpha$$-hydrogen (pKa ≈ 24-25).

Putting these facts together:

Least acidic           Most acidic
$$\text{(D) } \lt \text{(C) } \lt \text{(A) } \lt \text{(B)}$$

Therefore, the increasing order of acidity of the $$\alpha$$-hydrogen is indeed:

Option A which is: $$(D) < (C) < (A) < (B)$$