Let the unknown number be represented by \( x \).
According to the problem, we can set up the following equation based on the given statement:
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Four times the sum of a number and four is: \[ 4(x + 4) \]
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Two multiplied by two less than three times the number is: \[ 2(3x - 2) \]
Now, we can set these two expressions equal to each other: \[ 4(x + 4) = 2(3x - 2) \]
Next, let's simplify both sides of the equation.
Starting with the left side: \[ 4(x + 4) = 4x + 16 \]
Now simplify the right side: \[ 2(3x - 2) = 6x - 4 \]
Now we have the equation: \[ 4x + 16 = 6x - 4 \]
Next, we will isolate \( x \) by first moving all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 4x \) from both sides: \[ 16 = 6x - 4x - 4 \]
This simplifies to: \[ 16 = 2x - 4 \]
Now, add 4 to both sides: \[ 16 + 4 = 2x \] \[ 20 = 2x \]
Now, divide both sides by 2: \[ x = 10 \]
The solution to the problem is: \[ \boxed{10} \]