1. **State the problem:** Evaluate the expression $x^2 \cdot 3$ when $x=2$. 2. **Recall the order of operations (PEMDAS):** Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). 3. **Substitute $x=2$ into the expression:** $$2^2 \cdot 3$$ 4. **Calculate the exponent first:** $$2^2 = 4$$ 5. **Multiply the result by 3:** $$4 \cdot 3 = 12$$ 6. **Final answer:** $$12$$ The value of the expression when $x=2$ is 12.