The value of $\left(2\frac{1}{6} + 1\frac{13}{18} - \frac{1}{6}\right) \times 16 \div 4$ is:

$\frac{134}{9}$

$\left(2\frac{1}{6} + 1\frac{13}{18} - \frac{1}{6}\right) \times 16 \div 4$

= $\left(\frac{13}{6} + \frac{31}{18} - \frac{1}{6}\right) \times 4$

= $\frac{39 + 31 - 3}{18}\times 4$

= $\frac{67}{18}\times 4$

= $\frac{134}{9}$