Let total work = $144$ units.

X completes $1/3$ in $6$ days $\rightarrow$ full work in $18$ days; Y completes $1/3$ in $8$ days $\rightarrow$ full work in $24$ days; Z completes $3/4$ in $12$ days $\rightarrow$ full work in $16$ days.

X, Y, Z daily work = $8$, $6$, and $9$ units respectively.

Y alone in $8 \frac{2}{3}$ ($\frac{26}{3}$) days does $\frac{26}{3} \times 6 = 52$ units. Remaining work = $144 - 52 = 92$ units.

All three together do $23$ units/day $\rightarrow 92 \div 23 = 4$ days.

Hence, $n = 4$