1. **State the problem:** Find the solution set for the inequality $$2c \geq 12$$ given the replacement set $$R = \{2, 4, 6, 8, 10, 12, 14, 16\}$$. 2. **Write the inequality:** $$2c \geq 12$$. 3. **Isolate the variable:** Divide both sides by 2 to solve for $$c$$. $$\frac{\cancel{2}c}{\cancel{2}} \geq \frac{12}{2}$$ which simplifies to $$c \geq 6$$. 4. **Interpret the inequality:** We want all values of $$c$$ in the replacement set $$R$$ such that $$c$$ is greater than or equal to 6. 5. **Check each value in $$R$$:** - 2: $$2 \geq 6$$? No. - 4: $$4 \geq 6$$? No. - 6: $$6 \geq 6$$? Yes. - 8: $$8 \geq 6$$? Yes. - 10: $$10 \geq 6$$? Yes. - 12: $$12 \geq 6$$? Yes. - 14: $$14 \geq 6$$? Yes. - 16: $$16 \geq 6$$? Yes. 6. **Solution set:** $$\{6, 8, 10, 12, 14, 16\}$$. **Final answer:** The solution set for $$2c \geq 12$$ with $$R = \{2,4,6,8,10,12,14,16\}$$ is $$\boxed{\{6, 8, 10, 12, 14, 16\}}$$.