1. **State the problem:** Multiply the two numbers $426$ and $11$. 2. **Formula and rules:** Multiplication of whole numbers can be done using the standard algorithm where each digit of the second number multiplies the entire first number, and then the results are added with proper place value. 3. **Step-by-step multiplication:** Multiply $426$ by $1$ (the units digit of $11$): $$426 \times 1 = 426$$ Multiply $426$ by $1$ (the tens digit of $11$), shift one place to the left: $$426 \times 1 = 426 \Rightarrow 4260 \text{ (shifted by one place)}$$ 4. **Add the partial products:** $$\begin{array}{r} \phantom{0}426 \\ +4260 \\ \hline 4686 \end{array}$$ 5. **Final answer:** $$426 \times 11 = 4686$$ This method ensures accurate multiplication by breaking down the problem into simpler parts and combining the results.