y = 2 ( x - d ) ( x + d ) ( x +

Choice B is correct. An x-intercept of a graph in the xy-plane is a point on the graph where the value of $y$ is $0$. Substituting $0$ for $y$ in the given equation yields $0=2\left(x-d\right)\left(x+d\right)\left(x+g\right)\left(x-d\right)$. By the zero product property, the solutions to this equation are $x=d$, $x=-d$, $x=-g$, and $x=d$. However, $x=d$ and $x=d$ are identical. It's given that $d$ and $g$ are unique positive constants. It follows that the equation $0=2\left(x-d\right)\left(x+d\right)\left(x+g\right)\left(x-d\right)$ has $3$ unique solutions: $x=d$, $x=-d$, and $x=-g$. Thus, the graph of the given equation has $3$ distinct x-intercepts.

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.