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the first part "number increase by 6" translates to x + 6

equals translates to =

product of that number and 4 translates to (x + 6)4

x + 6 = (x +6)4

x + 6 = 4x + 24

6 = 3x + 24

-18 = 3x

x = -6

===================================

Another contributor interpreted the question differently:

x + 6 = 4x

Subtract 'x' from each side:

6 = 3x

Divide each side by 3:

x = 2

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