Let's analyze the given compound: $(NC{)}_{2}C=C(CN{)}_2$

The structure can be expanded as follows:

$\text{N equivC - C (=C) - C equivN}$
$\text{ | }$
$\text{C equivN}$
$\text{ | }$
$\text{C equivN}$

More clearly, it is:

$\text{N equivC}$
$\text{ | }$
$\text{C = C}$
$\text{ | }$
$\text{N equivC}$

With two $\text{CN}$ groups attached to each carbon of the $\text{C=C}$ double bond.

Let's count the $\sigma$ and $\pi$ bonds:

Step 1: Count $\sigma$ bonds (x)

• In each $\text{C equivN}$ group: 1 $\sigma$ bond. There are 4 such groups, so $4\times 1=4$ $\sigma$ bonds.
• Between the central carbons: 1 $\sigma$ bond (part of the $\text{C=C}$ double bond).
• Between each central carbon and its attached $\text{CN}$ groups: 2 $\sigma$ bonds per central carbon, so $2\times 2=4$ $\sigma$ bonds.
• Total $\sigma$ bonds (x) = $4+1+4=9$.

Step 2: Count $\pi$ bonds (y)

• In each $\text{C equivN}$ group: 2 $\pi$ bonds. There are 4 such groups, so $4\times 2=8$ $\pi$ bonds.
• Between the central carbons (in $\text{C=C}$ double bond): 1 $\pi$ bond.
• Total $\pi$ bonds (y) = $8+1=9$.

Step 3: Calculate $x\times y$

• $x=9$
• $y=9$
• $x\times y=9\times 9=81$.

Option Analysis:

• A) 20: Incorrect. This value does not match our calculation.
• B) 72: Incorrect. This value does not match our calculation.
• C) 81: Correct. This matches our calculated value of $9\times 9=81$.
• D) 64: Incorrect. This value does not match our calculation.

Correct Answer: (C)