Although it would be a hard question, this concept is certainly on the MCAT, and it is possible to see a similar question as a discrete. I can't really make it any simpler than what the explanation has got, but I can try to help you understand how they come up with this.
As you know, a charged sphere creates an electric field around it, like Earth creating a gravitational field around it. A charged particle will be acted on by the electric field, just like anything with mass will be subject to gravity on earth. And like the earth, when the particle changes position with respect to the source of the field (i.e. the charged sphere), its potential energy changes. Now, you know that potential energy due to earth's gravity is equal to mgh. By convention h is considered to be "ground-level" but it does not really matter because only change in potential energy has any meaning. Likewise, there is an expression for potential energy due to a charged sphere/particle/point. The only difference between "potential" and "potential energy" is that the latter term is dependent on the charge of the moving particle. In this problem, that is the particle with q = -4 x 10E-9. Potential is independent. Thus we can define a potential around one stationary charge without the need for the second charge. For an analogy, think of gravity. Gravity is present on the moon, even though there is nothing on the moon except an American flag.
The equation you absolutely need to know is the equation for potential, V=kQ/r where Q is the stationary charge, and r is the distance from (the center of) the charge. That means that every distance away from this charge, all the way out to infinity can be defined to have a certain potential due to this charge. Now potential energy takes this potential and also brings in the charge of the moving particle you are concerned about. So U = qV, where q is the charge of the particle that moves, not the particle that is stationary. Like gravity, electrostatic forces are conservative. That means that all potential energy is converted to kinetic energy and vice-versa. There is no loss of energy. Since there is a potential difference between two points in space, there must be a potential energy difference when a particle moves between these two points, and this difference must be converted all to kinetic energy. By the work-kinetic energy theorem, W = dKE = dU.
So what you have to do for this problem is figure out what the potential difference between X and Y is through V = kQ/r. Convert that to potential energy difference by multiplying it by the moving charge, q, which equals work. Now for sign conventions. Positive work signifies a gain in kinetic energy, while negative work is the opposite. Intuitively, you can see that the two charges are opposite in sign. Hence the electric field will bring them together naturally, raising the kinetic energy (or speed, if you want to see it that way) of the moving charge, and work done by the field is positive. Mathematically W done by an electric field is always -dU = -qdV = -KqQ d(1/r). You have to take the sign of all of these variables into account.
