Solubility of N-[(4-hydroxy-3-methoxyphenyl)methyl]acetamide at different pH
I would agree that it is most soluble in NaOH.

However, the molecule will only deprotonate the OH proton not the NH proton.  I wouldn't give your explanation much, if any, credit because you aren't saying which proton would deprotonate, and you are implying the molecule will lose all protons.

Also, at low enough pH the N will protonate, i.e. it would gain a second proton.