Check formulas. The starting material is C₁₆H₁₈O₃, whereas the product is C₁₅H₁₆O₃. Thus CH₂O₂ has been lost. Typically, relatively small molecules are lost during organic reactions. Thus we might consider the missing atoms as corresponding to CO and H₂O.

Now ask what fragments of the reactant structure are candidates to be lost? One obvious possibility is the aldehyde function at C-9, which would correspond to the CO lost.

A key to mapping one structure onto another is to look for an "anchor": a piece of structure that typically remains unchanged by common reaction processes. Benzene rings are anchors; very few reactions break them apart. Likewise, alkyl groups attached to benzene rings may be chemically modified, but very few reactions detach the benzylic carbon. Thus we consider the reactant benzene ring and its methoxyl substituent to be unchanged; likewise, C-1 and C-4.

With this reasoning, we map the rest of the atoms as indicated by the numbers. The molecule of water lost consists of O-1 and two hydrogens from C-8. A bond is to be made between C-8 and C-4, and the bond between C-3 and C-9 is broken.

The C-8 to C-4 bonding should now look like a familiar reaction type: the aldol condensation. The protic solvent mixture and strong base are certainly right for this kind of process.