Let $Y\subset l_{\infty }^{\left(n\right)}$ be a hyperplane and let $A\in ℒ\left(Y\right)$ be given. Denote $$\begin{array}{ccc}\hfill 𝒜=& \{L\in ℒ(l_{\infty }^{\left(n\right)},Y):L\mid Y=A\}\text{and}\hfill & \hfill {\lambda }_A=inf\{\parallel L\parallel :L\in 𝒜\}.\end{array}$$ In this paper the problem of calculating of the constant ${\lambda }_A$ is studied. We present a complete characterization of those $A\in ℒ\left(Y\right)$ for which ${\lambda }_A=\parallel A\parallel$. Next we consider the case ${\lambda }_A>\parallel A\parallel$. Finally some computer examples will be presented.