Process function to NAND and use only negative conjunction functions
$$Y = (X_1 \cdot X_2) + \overline {(X_3 \cdot \overline {X_1}) + X_2} $$ 

Double negation: \$ X =  \overline{\overline{X}}\$

$$Y = \overline {\overline {(X_1 \cdot X_2) + \overline {(X_3 \cdot \overline {X_1}) + X_2}}} $$ 

Take deMorgan's:

$$Y = \overline {\overline {(X_1 \cdot X_2)} \cdot \overline {\overline {(X_3 \cdot \overline {X_1}) + X_2}}} $$ 

Take deMorgan's on 2nd term:

$$Y = \overline {\overline {(X_1 \cdot X_2)} \cdot \overline {\overline {(X_3 \cdot \overline {X_1})} \cdot \overline {X_2}}} $$