Write the product of the quantity 2 more than quadruple a number and the quantity 4 less than the product of 6 and a number.

Okay, so to solve this we need to write some equations.

Let’s split it into two parts.

The quantity 2 more than quadruple a number

If we call a number x
Quadruple x would be x x 4 which is 4x and then 2 more would be to add two so you get 4x + 2.

Then to do the other half: 4 less than the Product of 6 and a number
So the product of 6 and the number is 6 x x which is x and then take away four so you get 6x -4

You want to find the product so you need to multiply the two expressions

(4x + 2)(6x - 4)

We can use foil to do this
F(irst) = 4x * 6x = 24x^2
O(uter) = -4 * 4x = -16x
I(nner) = 6x * 2 = 12 x
L(ast) = 2 * -4 = -8

Put it together to get
24x^2 -4x -8
Then you can solve this quadratic to get -0.5 and 2/3

Let me know if you have any questions