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Adding integers means combining their values together. Integers include both positive and negative numbers. When you add two integers, you follow specific rules:
1. Add their absolute values if both integers have the same sign (both are positive or both are negative).
2. Subtract the smaller absolute value from the larger absolute value if the integers have different signs. The result takes the sign of the integer with the larger absolute value.
For example, if you are adding -2 and -11, you add their absolute values: |2| + |11| = 2 + 11 = 13. Since both integers are negative, the result is -13. Integer addition becomes simple when you follow these rules consistently.

Negative numbers are numbers less than zero, represented with a minus sign ( - ) in front. They are crucial in real-world contexts, such as temperatures below freezing, debts, and levels below sea level. Here are some important properties:
- Adding a negative number is like subtracting its absolute value.
- Subtracting a negative number is like adding its absolute value.
- Multiplying two negative numbers gives a positive number.
For instance, in the exercise step \( -2 + (-11) \), when adding -11 to -2, you are actually moving 11 units more to the left of -2 on the number line, leading to a result of -13. Understanding how to work with negative numbers helps simplify many mathematical problems.

Breaking down problems into steps makes them easier to solve. Let's revisit the problem using a step-by-step approach:
Step 1: Solve the First Pair
Calculate the sum of the first pair \[ -2 + (-11) \].Then, \[ -2 + (-11) = -13 \].
Step 2: Solve the Second Pair
Calculate the sum of the second pair \[ 12 + (-2) \].Then, \[ 12 + (-2) = 10 \].
Step 3: Solve the Third Pair
Calculate the sum of the third pair \[ 18 + (-6) \].Then, \[ 18 + (-6) = 12 \].
Step 4: Add All Results
Add up all the results obtained from each pair. So, \[ -13 + 10 + 12 = 9 \].
By following clear steps, we systematically solve the problem, ensuring accuracy and understanding at each stage.