Answer
The number is $4$.
Work Step by Step
Let
$x$ = the unknown number
Then
"a number increased by 12" means $x+12$
"four times a number" means $4x$
Thus, the equation that represents the situation is:
$x+12=4x$
Subtract $x$ on both sides of the equation to obtain:
$12=4x-x
\\12=3x$
Divide $3$ on both sides of the equation to obtain:
$\dfrac{12}{3} = x
\\4 = x$