Four times a number, diminished by 6, yields the same result as twice the same number increased by 4. Find the number.

just translate the English into Math,

4x - 6 = 2x + 4

then solve for x

4 n - 6 = 2 n + 4

2 n = 10

n =5

4x-6=2x+4

To solve this equation, let's assign a variable to the unknown number. Let's call the number "x".

According to the problem, "Four times a number, diminished by 6, yields the same result as twice the same number increased by 4." We can translate this into the following equation:

4x - 6 = 2x + 4

To find the value of x, let's isolate the variable on one side of the equation. We can do this by performing algebraic operations:

4x - 2x = 4 + 6

2x = 10

Now, divide both sides of the equation by 2 to solve for x:

x = 10/2

Simplifying the expression, we find:

x = 5

Therefore, the number is 5.