  This paper studies the Kazhdan-Lusztig coefficients $\mu(u,w)$ of the
Kazhdan-Lusztig polynomials $P_{u,w}$ for the lowest cell ${c_{0}}$ of an
affine Weyl group of type $\widetilde{G_{2}}$ and gives an estimation
$\mu(u,w)\leqslant 3$ for $u,w\in c_{0}$.
