The equation 40 x + 20 y = 160 represents the number of sweaters, x ,

Choice B is correct. It's given that the equation $40x+20y=160$ represents the number of sweaters, $x$, and the number of shirts, $y$, that Yesenia purchased for $\$160$. If Yesenia purchased $2$ sweaters, the number of shirts she purchased can be calculated by substituting $2$ for $x$ in the given equation, which yields $40\left(2\right)+20y=160$, or $80+20y=160$. Subtracting $80$ from both sides of this equation yields $20y=80$. Dividing both sides of this equation by $20$ yields $y=4$. Therefore, if Yesenia purchased $2$ sweaters, she purchased $4$ shirts.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the number of shirts Yesenia purchased if she purchased $0$ sweaters.

Choice D is incorrect. This is the price, in dollars, for each sweater, not the number of shirts Yesenia purchased.