Four times the square of a certain number increased by 6 times the number equals 108 find the number

A few key words you should know:
"times" means to multiply
"square" means a number multiplied by itself
"increased by" means to add

With these words in mind, you can translate the wording into an equation. Let's represent the unknown number as "x."

The wording of the question is extremely ambiguous because there are multiple ways to interpret almost every part of the question "increased by 6 times the number." Is the expression increased by 6x? Or increased by 6, then multiplied by x?

4 * (x^2) + 6x = 108
4x^2 + 6x - 108 = 0
x = -6, 4.5

[4 * (x^2) + 6 ]*x = 108
(4x^2 + 6)x = 108
4x^3 + 6x =108
4x^3 + 6x - 108 = 0
Plotting this equation on a graphing calculator, the zero is found when
x = 2.834

The question asks to "find the number," and the second way yields only one solution, which suggests the second way: x = 2.834.