The number is $10$.
Work Step by Step
First, let's translate this statement into an algebraic equation we can solve. Let's first break it into its component parts. "$6$ times a number" is $6x$. "Decreased by $20$" means to subtract $20$. "Is $4$ times the number" means $ = 4x$. Now, let's put the components together to make an equation: $$6x - 20 = 4x$$ Add $20$ to each side to move the constant to one side of the equation: $$6x = 4x + 20$$ Subtract $4x$ from each side to isolate variables to the other side of the equation: $$2x = 20$$ Divide both sides by $2$ to solve for $x$: $$x = 10$$ The number is $10$.