In triangle ABC, AB = AC, and AD is the perpendicular from A to BC…

Step 1. The equal parts.

1. $\angle ADB = \angle ADC = 90^\circ$, because $AD$ is perpendicular to $BC$.
2. $AB = AC$, given. These are the hypotenuses.
3. $AD = AD$, the common side.

Step 2. The rule. $\triangle ABD \cong \triangle ACD$ by RHS. So $BD = DC$ and $\angle BAD = \angle CAD$ by CPCT.

Step 3. The number. In triangle $ABD$, $\angle ABD = 180^\circ - 90^\circ - 24^\circ = 66^\circ$.