Step 1: Concept
Stoichiometry allows us to calculate the amount of products formed from a given amount of reactants using the balanced chemical equation.
Step 2: Molar Ratio Analysis
From the balanced equation: $2$ moles of $C_{4}H_{10}$ produce $8$ moles of $CO_{2}$. This simplifies to a ratio of $1:4$.
Step 3: Calculation
If $1$ mole of butane produces $4$ moles of $CO_{2}$, then $3$ moles of butane will produce $3 \times 4 = 12$ moles of $CO_{2}$.
Step 4: Conclusion
The amount of $CO_{2}$ formed is $12$ moles.
Final Answer: (B)