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Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Equations: - Equations are the statements in which two expressions are equal. The expression can be created by variables, constants, numbers and symbols.

The given problem is:

The sum of one half of a number and 6 equals one third of a number.

Let the number be x.

The given problem can be written in the form of an equation as

$\frac{1}{2}x+6=\frac{1}{3}x$

Add $鈭�6鈭�\frac{1}{3}x$to both sides of the equation.

$\begin{array}{l}\frac{1}{2}x+6鈭�6鈭�\frac{1}{3}x=\frac{1}{3}x鈭�6鈭�\frac{1}{3}x\\ \frac{1}{2}x鈭�\frac{1}{3}x=鈭�6\\ \frac{3鈭�2}{6}x=鈭�6\\ \frac{x}{6}=鈭�6\end{array}$

Multiply 6 to both sides of the equation.

$\begin{array}{l}\left(6\right)脳鈭�\frac{x}{6}=6脳\left(鈭�6\right)\\ x=鈭�36\end{array}$

Hence, the number is $鈭�36$.