To predict $y$ from $x$, only 8 parameters are needed - w.l.o.g. $P(y|x_1,x_2,x_3),P(y|!x_1,x_2,x_3),P(y|x_1,!x_2,x_3),P(y|!x_1,!x_2,x_3),P(y|x_1,x_2,!x_3),P(y|!x_1,x_2,!x_3),P(y|!x_1,x_2,!x_3),P(y|x_1,!x_2,!x_3),P(y|!x_1,!x_2,!x_3)$.

The answer in the solution was 15 - there are 7 other parameters (w.l.o.g. $P(x_1), P(x_2|x_1), P(x_2|!x_1), P(x_3|x_2,x_1), P(x_3|!x_2,x_1), P(x_3|x_2,!x_1), P(x_3|!x_2,!x_1)$), but

they are irrelevant as you are already given $x$.