Like terms

The test

Two terms are alike when their variable parts match exactly. The coefficients can be anything.

Terms	Alike?	Why
$3x$ and $5x$	yes	both are “some number of $x$”
$3x$ and $3x^2$	no	different powers
$3x$ and $3y$	no	different variables
$3x$ and $7$	no	one has a variable, one does not
$2xy$ and $-5xy$	yes	identical variable part $xy$

Combining them

Add or subtract the coefficients and keep the variable part unchanged:

$$4x - 2x = 2x$$

It works because $4x$ means four of something and $2x$ means two of the same something. Removing two leaves two.

Why unlike terms cannot combine

$2x + 12$ cannot become $14x$. You do not know what $x$ is, so “two of something” plus “twelve” has no single simpler form — it is like adding two apples to twelve, which is not fourteen apples. Leaving an expression as $2x + 12$ is a finished answer, not an unfinished one.