The product of a positive number x and the number that is 8 more than x

Choice B is correct. The number that's $8$ more than $x$ can be represented by the expression $x+8$. It's given that the product of $x$ and $x+8$ is $180$, so it follows that $\left(x\right)\left(x+8\right)=180$, or $x^2+8x=180$. Subtracting $180$ from each side of this equation yields $x^2+8x-180=0$. Factoring the left-hand side of this equation yields $\left(x-10\right)\left(x+18\right)=0$. Applying the zero product property to this equation yields two solutions: $x=10$ and $x=-18$. Since $x$ is a positive number, the value of $x$ is $10$.

Choice A is incorrect. If $x=5$, the product of $x$ and the number that's $8$ more than $x$ would be $\left(5\right)\left(13\right)$, or $65$, not $180$.

Choice C is incorrect. This is the value of the number that's $8$ more than $x$, not the value of $x$.

Choice D is incorrect. If $x=36$, the product of $x$ and the number that's $8$ more than $x$ would be $\left(36\right)\left(44\right)$, or $\mathrm{1,584}$, not $180$.