Reaction of dimethyl sulfate with Protocatechualdehyde
When one equivalent of dimethyl sulfate reacts with 3,4-dihydroxybenzaldehyde (protocatechualdehyde), there are two nucleophilic sites in the molecule, namely 3- and 4-hydroxy-groups. If one equivalent of strong base such as $\ce{NaOH}$ is used, it will deprotonate the most acetic group between them, in this case, 4-hydroxy-group. For example, $\mathrm{p}K_\mathrm{a}$ of 4-hydroxybenzaldehyde is $7.61$ while $\mathrm{p}K_\mathrm{a}$ of 3-hydroxybenzaldehyde is $8.98$ at $\pu{25 ^\circ C}$ (Ref.1). Thus, it is safe to assume that product K is 3-hydroxy-4-methoxybenzaldehyde (isovanillin).

However, the regioselectivity of the synthesis (when two nucleophilic sites are present) can be controlled by the number of base equivalents in this kind of alkylation steps (Ref.2). Thus, in excess $\ce{NaOH}$, both phenolic hydroxy groups of 3,4-dihydroxybenzaldehyde would be deprotonated and methylation would occur at 3-phenolate, because it is the most reactive at this point between two (basically, negative charge of 4-phenolate should be largely delocalized within aromatic nucleus with benzaldehyde group than that of 3-phenolate without direct resonance effect from benzaldehyde group).  Therefore, the major product M in this case would be 4-hydroxy-3-methoxybenzaldehyde (vanillin). You can probably compare with methylation of ascorbic acid in different conditions.

Note: Some literature mentioned that when one equivalent of $\ce{NaOH}$ is used, reaction is must faster and tends to use both methyl groups of dimethyl sulfate. Thus, I won't surprised if the given answer for K is 3,4-dimethoxybenzaldehyde.

References:


E. P. Serjeant, Boyd Dempsey, Editors, IUPAC chemical data series no. 23: Ionization Constants of Organic Acids in Aqueous Solution; Pergamon: Oxford, United Kingdom, 1979 (Values extracted from PDF here).
Tobias Schneider, Vladimir Kubyshkin, Nediljko Budisa, "Synthesis of a Photo‐Caged DOPA Derivative by Selective Alkylation of 3,4‐Dihydroxybenzaldehyde," Eur. J. Org. Chem. 2018, (18), 2053-2063 (https://doi.org/10.1002/ejoc.201701749).