Answer: [B] $7.76k$

Explanation:1. Let $M\_{80}$ be the mass at $80$ days old and $M\_{160}$ be the mass at $160$ days old. We are given $M\_{80} = k$ grams.

2. Understand percent increase: Percent increase is calculated as $\dfrac{\text{Amount of Increase}}{\text{Original Amount}} \times 100\%$. The amount of increase is $M\_{160} - M\_{80}$. So, $676\% = \dfrac{M\_{160} - k}{k} \times 100\%$.

3. Convert the percentage to a decimal: $676\% = \dfrac{676}{100} = 6.76$.

4. Set up the equation for the increase: Amount of Increase = Percent Increase (as decimal) $\times$ Original Amount. Amount of Increase = $6.76 \times k = 6.76k$.

5. Calculate the new mass $M\_{160}$: New Mass = Original Mass + Amount of Increase. $M\_{160} = k + 6.76k$.

6. Simplify the expression: $M\_{160} = (1 + 6.76)k$. $M\_{160} = 7.76k$.

Alternatively, if a quantity increases by $P\%$, the new quantity is $(1 + \dfrac{P}{100}) \times \text{Original Quantity}$. New Mass = $(1 + \dfrac{676}{100}) \times k$ New Mass = $(1 + 6.76) \times k$ New Mass = $7.76k$.

7. Match with the given options: The expression representing the mass at $160$ days old is $7.76k$. This corresponds to option [B].

Conclusion:The expression representing the red kangaroo's mass at $160$ days old is $7.76k$.