How many sigma and pi bonds are in benzene?

I count:

• #bb6 xx (sp^2)# #"C"-"C"# sigma (#sigma#) bonds
• #bb6 xx (sp^2)# #"C"-"H"# sigma (#sigma#) bonds
• #bb3 xx (sp^2)# #"C"="C"# pi (#pi#) bonds

Benzene is an aromatic compound, one of whose major resonance structures is depicted like so:

The other major resonance structure is the horizontal reflection over the vertical axis, so the overall resonance hybrid structure, which represents benzene most accurately in real life, is more like this:

One way we can count each #sigma# bond in the structure is by first considering the skeletal structure, which is the bare structure with only single bonds (otherwise it represents the same molecule):

(all implicit hydrogens are shown. There are no other implicit hydrogens in the full structure.)

From this, recall that one single bond contains one sigma bond. The sigma (#sigma#) bonds are simply the number of single bonds shown here:

• #6 xx (sp^2)# #"C"-"C"# sigma (#sigma#) bonds
• #6 xx (sp^2)# #"C"-"H"# sigma (#sigma#) bonds

Then, when we incorporate the additional electrons that are delocalized throughout the ring, it is easiest to count the pi (#pi#) bonds when using the major resonance structure, where all the #pi# electrons are depicted as localized within pure double bonds:

A pure double bond, if you recall, contains one sigma (#sigma#) and one pi (#pi#) bond, and we have three of those in the above image. Since we already counted those #sigma# bonds, we only count the #pi# bonds here.

We've accounted for all the #sigma# and #pi# bonds at this point, so in the end we have:

• #bb6 xx (sp^2)# #"C"-"C"# sigma (#sigma#) bonds
• #bb6 xx (sp^2)# #"C"-"H"# sigma (#sigma#) bonds
• #bb3 xx (sp^2)# #"C"="C"# pi (#pi#) bonds