Think of an equation as a teeteer-totter or see-saw. If both sides are equally weighted, it will stay centered but if one side is heavier than the other, that side will drop to the ground showing the imbalance.
Equations, by definition, are always equal on both sides. Thus, if something is added or subtracted from one side, it must also be added or subtracted from the other to maintain equality. The same applies to multiplication and division. Do unto one side the same as you do unto the other side.
The goal of manipulating equations is to end up with the equation in a form that is helpful in finding a solution.
Examples:
\(\color{Red}\textbf{2x-6=4}\) —This is the original equation
\(\color{Red}\textbf{2x-6-4=4-4}\) —Now subtract 4 from BOTH sides
\(\color{Red}\textbf{2x-10=0}\) —Giving a simpler equation
\(2x-10+10=+10\) —Next add 10 to both sides
\(2x=10\) —Now its even simpler
\(\frac{2x}{2}=\frac{10}{2}\) —Divide both sides by 2
\(x=5\) —Ta Da — Finished. x = 5