1. **State the problem:** Multiply the expressions $2x^3$ and $3x^4$. 2. **Formula and rules:** When multiplying terms with the same base, multiply the coefficients and add the exponents: $$a x^m \times b x^n = (a \times b) x^{m+n}$$ 3. **Apply the formula:** Multiply the coefficients: $2 \times 3 = 6$. 4. Add the exponents of $x$: $3 + 4 = 7$. 5. **Final expression:** $$6x^7$$ So, $2x^3 \times 3x^4 = 6x^7$.