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When simplifying algebraic expressions, it's important to follow the order of operations. This is sometimes remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), and Addition and Subtraction (left to right). When you see an expression, follow these steps:

First, handle any calculations inside parentheses.
Next, evaluate any exponents.
Then, perform multiplication and division from left to right.
Finally, do any addition and subtraction from left to right.

For the expression -12+(7-8x)+6, we start by simplifying inside the parentheses: 7-8x.

The distributive property is a useful tool in algebra. It states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products. Formally, the distributive property is written as: \[ a(b+c) = ab + ac \].

When we see expressions in parentheses added to other numbers, we can distribute multiplication over addition or subtraction. However, if there is no multiplication, you can simply distribute the process of combining like terms as shown in -12+(7-8x)+6.
Here, the steps would be:

- Distribute and combine constants: \ -12 + 7 - 8x + 6 \- Simplify combining the constants: -12 + 7 + 6, resulting in 1 - 8x.

This way, you are making sure to consider all terms properly.

Combining like terms is essential when simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, but 3x and 3 are not.

To combine like terms, follow these steps:

• Identify terms with the same variable.
• Add or subtract the coefficients (numbers in front of the variables).

In the expression -12+(7-8x)+6, like terms are the constant numbers (-12, 7, and 6).

Here’s how you do it:

• Add constants first: -12 + 7 + 6 = 1.
• Then combine with the remaining variable term: 1 - 8x.

This gives you the simplified expression.