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I'm guessing you mean the absolute value of (4x - 6) when you type /4x-6/
To solve this equation, you solve the following two equations:
4x-6 = 5 and 4x-6 = -5
You do this because |5| = 5, and |-5| = 5.
The first one gives 4x = 11, which means x = 11/4.
The second one gives 4x = 1, which means x = 1/4.
So x = 11/4, or x = 1/4.

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(Please ignore all dotted lines [---] in the pictures. They are there so the picture would come out right.)
Suppose your original square has side length x:
_____
|-------|
|-------| x
|_____|
x (not to scale)
Then its area is . Doubling the base gives the following shape:
__________
|-------------|
|-------------| x
|__________|
2x (not to scale)

Shrinking the height by 3 inches gives the following shape:

__________
|-------------| x-3
|__________|
2x (not to scale)

The area of this new rectangle is .
This area is 40 square inches larger than the area of the original square.
Recall that the area of the original square is .
This gives us the equation .
Subtracting from both sides gives .
Then we subtract 40 from both sides to get .
We can factor this into , which means x = 10 or
x = -4.
Since x represents the length of the side of a square, x cannot be less than zero. Hence, x = 10 inches.

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When finding the amount of square feet needed to cover a room, you should find the area of the given room. In this case the room is 10ft by 12ft, so the area is .
The second part is asking how many feet of base board you need to cover the perimeter of the room. The perimeter P of a rectangular room is given by , where a and b are the lengths of the sides. In this case, a = 12ft and b = 10ft (you could reverse these but it doesn't matter), so the perimeter P is . So Jim needs 44ft of base board.