Term

Finding the terms

Split at every $+$ and $-$, and keep each sign with the piece that follows it:

$$4x + 12 - 2x$$

The terms are $4x$, $+12$ and $-2x$. Carrying the sign along is what keeps combining like terms from going wrong.

Multiplication does not separate terms

$4xy$ is one term, not two. Multiplication and division bind a term together; only addition and subtraction split one from the next. Similarly $\tfrac{3x}{5}$ is a single term.

Terms inside parentheses

In $4(x + 3)$ everything in the parentheses is part of one term until you distribute. That is why you cannot start combining anything with the $x$ inside them while the parentheses are still there — see multi-step equations.