The given expression is:

$4 + \left( (14 - 4) \div 2 \right) \times 3$

We will solve step by step, following the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right)).

Step 1: Solve inside the parentheses

$(14 - 4) = 10$ So the expression becomes: $4 + \left( 10 \div 2 \right) \times 3$

Step 2: Division

$10 \div 2 = 5$ Now the expression becomes: $4 + 5 \times 3$

Step 3: Multiplication

$5 \times 3 = 15$ Now the expression becomes: $4 + 15$

Step 4: Addition

$4 + 15 = 19$

Final Answer:

$\boxed{19}$

Let me know if you would like further clarification! Here are some follow-up questions to explore:

1. Why is it important to follow the order of operations in mathematical expressions?
2. How would the result change if parentheses were placed differently in the problem?
3. Can you create a similar problem that results in a different answer?
4. What happens if division by zero occurs in a similar problem?
5. How does understanding PEMDAS help in solving complex algebraic equations?

Tip: Always double-check the placement of parentheses as they can significantly change the result of an expression!