Let's simplify each expression one by one.

a) $-13 + 6 - 13 + 6$

Step 1: Combine the terms that involve addition or subtraction. $-13 + 6 = -7$ $-13 + 6 = -7$

Step 2: Now add the results. $-7 + (-7) = -14$

So, the simplified answer is: $\boxed{-14}$

b) $-13 - 6 - 13 - 6$

Step 1: Combine the terms that involve subtraction. $-13 - 6 = -19$ $-13 - 6 = -19$

Step 2: Now add the results. $-19 + (-19) = -38$

So, the simplified answer is: $\boxed{-38}$

c) $-13 + (-6) - 13 + (-6)$

Step 1: Simplify each pair of terms. $-13 + (-6) = -19$ $-13 + (-6) = -19$

Step 2: Now add the results. $-19 + (-19) = -38$

So, the simplified answer is: $\boxed{-38}$

d) $-13 - (-6) - 13 - (-6)$

Step 1: Simplify the double negative terms. $-13 - (-6) = -13 + 6 = -7$ $-13 - (-6) = -13 + 6 = -7$

Step 2: Now add the results. $-7 + (-7) = -14$

So, the simplified answer is: $\boxed{-14}$

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Would you like more details on any of the steps or have any follow-up questions?

Here are 5 related questions:

1. What happens when you add two negative numbers together?
2. How do you handle subtraction of negative numbers?
3. Can you simplify $5 - (-3)$?
4. What is the result of adding a positive and a negative number together?
5. How does the distributive property apply to expressions with negative numbers?

Tip: Remember that subtracting a negative number is the same as adding its positive counterpart!