For the given expression, identify the terms, like terms, coefficients, and constant terms. Then simplify the expression:

To analyze the expression \(-1 + 4x + 6x - 20\), we can identify the different components:

1. **Terms:** The expression consists of the following terms:
- \(-1\) (constant term)
- \(4x\) (variable term)
- \(6x\) (variable term)
- \(-20\) (constant term)

2. **Like terms:** Like terms are terms that have the same variable raised to the same power. In this case, the like terms are:
- \(4x\) and \(6x\) (both terms containing the variable \(x\))
- \(-1\) and \(-20\) (constant terms)

3. **Coefficients:** The coefficients are the numerical factors in front of the variable terms:
- The coefficient of \(4x\) is \(4\).
- The coefficient of \(6x\) is \(6\).
- The constant terms \(-1\) and \(-20\) do not have coefficients associated with any variable.

4. **Constant terms:** The constant terms in the expression are \(-1\) and \(-20\).

Now, to **simplify** the expression, we will combine like terms.

The variable terms \(4x\) and \(6x\) can be combined:
\[
4x + 6x = 10x
\]

The constant terms \(-1\) and \(-20\) can also be combined:
\[
-1 - 20 = -21
\]

Putting it all together, the simplified expression is:
\[
10x - 21
\]

Thus, the final simplified form of the expression \(-1 + 4x + 6x - 20\) is:
\[
\boxed{10x - 21}
\]