$\begin{array}{1 1}(a)\;20102years&(b)\;22694years\\(c)\;23257.46years&(d)\;21262.5years\end{array}$

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Carbon decay will follow first order kinetics.

So $t_{1/2}=\large\frac{ln\;2}{K}$

$K=\large\frac{ln \;2}{5730years}$

$K\times t=ln\large\frac{a}{a-x}$

$K\times t=ln\large\frac{1}{1-x/a}$

Here $x/a=0.94$

$\large\frac{ln\;2}{5730}$$t=ln\large\frac{1}{1-0.94}$

$\large\frac{ln\;2}{5730}$$t=ln\large\frac{1}{0.06}$

$t=23257.46years$

Hence (c) is the correct answer.

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