1. **State the problem:** Simplify the expression $$\frac{2}{4r+3} \times \frac{28r+21}{r}$$. 2. **Rewrite the expression:** $$\frac{2}{4r+3} \times \frac{28r+21}{r} = \frac{2(28r+21)}{r(4r+3)}$$ 3. **Factor the numerator:** Notice that $$28r+21$$ has a common factor of 7: $$28r+21 = 7(4r+3)$$ 4. **Substitute the factorization:** $$\frac{2 \times 7(4r+3)}{r(4r+3)}$$ 5. **Cancel the common factor $4r+3$:** $$\frac{2 \times 7 \cancel{(4r+3)}}{r \cancel{(4r+3)}} = \frac{14}{r}$$ 6. **Final simplified expression:** $$\boxed{\frac{14}{r}}$$ This means the original expression simplifies to $$\frac{14}{r}$$, provided $$r \neq 0$$ and $$4r+3 \neq 0$$ to avoid division by zero.