Consider $\Delta BCE$ and $\Delta DCF$.
$\begin{array}{rcll}
BC & = & DC & \text{(property of rhombus)}\\
\angle CBE & = & \angle CDF & \text{(property of rhombus)} \\
AD & = & AD & \text{(property of rhombus)} \\
BE & = & AB – AE \\
& = & AD – AF & \text{(given)} \\
& = & DF
\end{array}$
Therefore, $\Delta BCE \cong \Delta DCF\ \text{(S.A.S.)}$.
Hence, we have $CE = CF\ \text{(corr. sides, $\cong \Delta$)}$.
Since $AE = AF$ and $CE = CF$, $AECF$ is a kite. Therefore, $\angle AEC = \angle AFC$. Hence, we have
$\begin{array}{rcll}
\angle AEC + \angle AFC + \angle EAF + \angle ECF & = & 360^\circ & \text{($\angle$ sum of polygon)} \\
2\angle AEC & = & 360^\circ – 42^\circ – 110^\circ \\
\angle AEC & = & 104^\circ
\end{array}$
Therefore, we have
$\begin{array}{rcll}
\angle BEC & = & 180^\circ – \angle AEC & \text{(adj. $\angle$s on a st. line)} \\
\angle BEC & = & 180^\circ – 104^\circ \\
\angle BEC & = & 76^\circ
\end{array}$
