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I understand the fact that the molecule has a principal axis of rotation of C6 however when following the point gorup flow chart why is the answer to the second question NO when it contains two C3 axis? Hence the answer should be a YES right? (I understand the molecule has C2 axis as well) Point group flow chart

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    $\begingroup$ Only different axes count. $\endgroup$ Commented Feb 26, 2016 at 10:52
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    $\begingroup$ Also, you chart seems to miss the groups $T,\;T_h,\;O,\;\text{ and }I$. $\endgroup$ Commented Feb 26, 2016 at 10:57
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    $\begingroup$ As @IvanNeretin stated - There's rather 1 C6 axis, than 2 C3 axis $\endgroup$
    – lcnittl
    Commented Feb 26, 2016 at 11:24

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Does it have two or more $C_2$ axes with $n>2$?

This question is asking if there is more than one $C_{n>2}$ axis not if there is more than one $C_{n>2}$ symmetry operation.

Yes, benzene has some $C_3$ operations. However, as pointed out in the comments, the $C_3$ axis lies along the $C_6$ axis - both run through the center of the ring perpendicular to the plane of the molecule. This axis is also a $C_2$ axis. There is only one $C_{n>2}$ axis - it just happens to be both a $C_6$ and a $C_2$ axis. All other rotation axes in benzene are $C_2$.

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