1. **State the problem:** We need to find the product of $2x$ and $3$. 2. **Formula used:** Multiplication of algebraic terms is done by multiplying the coefficients and keeping the variable part. 3. **Calculate the product:** $$2x \times 3 = 2 \times 3 \times x = 6x$$ 4. **Explanation:** Multiplying $2x$ by $3$ means multiplying the number $2$ by $3$ and then attaching the variable $x$ to the result. 5. **Final answer:** $$6x$$