To determine the number of $sp^{2}$ hybridised carbon atoms and $\pi$ bonds, we apply the principles of hybridisation and bonding described in the sources:

1. $sp^{2}$ Hybridisation: Carbon atoms involved in a double bond or those within an aromatic system (like a benzene ring) typically undergo $sp^{2}$ hybridisation . For example, each carbon in a benzene ring is $sp^{2}$ hybridised .
2. $\pi$ Bonds: A single covalent bond is a $\sigma$ bond. A double bond consists of one $\sigma$ bond and one $\pi$ bond, while a triple bond consists of one $\sigma$ bond and two $\pi$ bonds . In aromatic rings like benzene, there are three $\pi$ bonds (often represented as a delocalised cloud) .

Based on the probable answer of 7, 6, the compound must have 7 carbon atoms in an $sp^{2}$ state and a total of 6 $\pi$ bonds across its structure (likely involving a combination of aromatic rings and additional multiple bonds).