To determine the number of carbon atoms in the reactants of the given chemical equation, we need to look at the compounds on the left side of the equation:
\[ 2C_6H_{10} + 17O_2 \]
The term \( C_6H_{10} \) indicates that each molecule of \( C_6H_{10} \) contains 6 carbon atoms. Since there are 2 molecules of \( C_6H_{10} \), we multiply the number of carbon atoms per molecule by the number of molecules:
\[ 2 \times 6 = 12 \]
Therefore, in the reactants, there are 12 atoms of carbon.
The answer is: 12 atoms.
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