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**Hint:**Here in this question, the given equation is the algebraic variable expressions having variable x. Here we have to write the given expression to the simplest form. First remove parenthesis by using sign convention, next identify the like terms and further simplify by using basic mathematics operations to get the required solution.

**Complete step-by-step solution:**

A variable expression is a combination of numbers or (constants), operations, and variables. Otherwise variable expressions are expressions that involve variables, which are symbols that represent changing quantities. The value of the expression will change as the value of the variable changes.

Now, consider the given variable expression

\[ \Rightarrow \,\,\,4x - 2 + \left( { - 6x} \right) + 8\]

Here x has a variable.

Firstly, remove brackets or parenthesis in the expression by using sign convention. As we know the multiplication of ‘+ ve’ sign and ‘- ve’ sign is ‘-ve’. Then the given expression can be written as

\[ \Rightarrow \,\,\,4x - 2 - 6x + 8\]

Identify the like terms, here 4x and -6x are the terms having variable x and -2 and 8 are the constant terms.

Always we operate the like terms only.

\[ \Rightarrow \,\,\,4x - 6x - 2 + 8\]

On simplification we get

\[ \Rightarrow \,\,\, - 2x + 6\]

Take 2 as common, then

\[ \Rightarrow \,\,\,2\left( { - x + 3} \right)\]

Or it can be written as

\[ \Rightarrow \,\,\,2\left( {3 - x} \right)\]

Hence, the simplest form of the given variable expression \[4x - 2 + \left( { - 6x} \right) + 8\] is \[2\left( {3 - x} \right)\].

**Note:**The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The alphabets are known as variables. The x, y, z etc., are called as variables. The numerals are known as constants. The numeral of a variable is known as co-efficient. We have 3 types of algebraic expressions namely monomial expression, binomial expression and polynomial expression. By using the arithmetic operations we can solve the equation.

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