1. **State the problem:** We are given a custom operation defined as $x \triangle y = 2x + 3y$. 2. **Given:** $A \triangle 3 = 21$. We need to find the value of $A$. 3. **Use the formula:** Substitute $x = A$ and $y = 3$ into the operation: $$A \triangle 3 = 2A + 3 \times 3$$ 4. **Simplify:** $$2A + 9 = 21$$ 5. **Solve for $A$:** $$2A = 21 - 9$$ $$2A = 12$$ 6. **Divide both sides by 2:** $$\cancel{2}A = \frac{12}{\cancel{2}}$$ $$A = 6$$ 7. **Final answer:** $A = 6$ which corresponds to option D.