${~K}_{600}=x \times 10^{-6} {~s}^{-1}$

${E}_{{a}}=209 {~kJ} / {mol}$

Applying ;

$\log \left(\frac{{K}_{{T}_{2}}}{{~K}_{{T}_{1}}}\right)=\frac{-{E}_{{a}}}{2.303 {R}}\left(\frac{1}{{~T}_{2}}-\frac{1}{{~T}_{1}}\right)$

$\log \left(\frac{{K}_{700}}{{~K}_{600}}\right)=\frac{-{E}_{{a}}}{2.303 {R}}\left(\frac{1}{700}-\frac{1}{600}\right)$

$\log \left(\frac{6.36 \times 10^{-3}}{{~K}_{600}}\right)=\frac{+209 \times 1000}{2.303 \times 8.31}\left(\frac{100}{700 \times 600}\right)$

$\log \left(6.36 \times 10^{-3}\right)-\log {K}_{600}=2.6$

$\Rightarrow \log {K}_{600}=-2.19-2.6=-4.79$

$\Rightarrow {K}_{600}=10^{-4.79}$

$=1.62 \times 10^{-5}$

$=16.2 \times 10^{-6}$

$=x \times 10^{-6}$

$\Rightarrow {x}=16$