$Y = ABC +B\overline{C}D + \overline{A}BC$

$Y =ABC + B\overline{C}D + \overline {A}BC$

$= BC + B\overline{C}D \hspace{2cm} since\hspace{.2cm} (A+\overline{A})=1$

$= B(C+\overline{C}D)$

$=B(B+D) \hspace{2.2cm} since\hspace{.2cm}A+\overline{A}B=A+B$

Which is required expression the realization of this expression is as shown below