[Assume steady state heat conduction]
\(\frac{\Delta T _{1}}{\Delta T _{2}}=\frac{\ell_{1}}{ k _{1}} \times \frac{ k _{2}}{\ell_{2}}=\frac{16}{ k _{1}} \times \frac{ k }{8}\)
\(\frac{20}{80}=\frac{16}{ k _{1}} \times \frac{ k }{8} \rightarrow k _{1}=8 k\)