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When rewriting equations it's important to make the **the same operation on both sides** to ensure that the equality still holds. So, if one side is divided by a number, the other side must be divided by the same number. In the equation $3x=12$ both sides is divided by $3$ to solve for $x.$ $\dfrac{3x}{{\color{#FF0000}{3}}}=\dfrac{12}{{\color{#FF0000}{3}}} \quad \Leftrightarrow \quad x=4$
Remember that division by zero is undefined, so, for example, by dividing both sides by $x$ it is assumed that $x$ cannot be zero.