In this example, it would be a motivating operation. To understand why, it is also important to understand why it is not the other three options:
Extinction is the diminishing of a particular behavior. To offer a hypothetical example: under motivational behavioral theories, if there is a behavior that we do not wish to see occurring in a student, such as outbursts during class, we may reward the student when sitting quietly or punish the student when such outbursts occur. Both cases are designed to stop the outbursts. Once the outbursts have ended, we would say that behavior is "extinct." In the scenario you have provided, it does not seem that there is a behavior we are trying to stop, so extinction does not apply.
A negative reinforcement is an action taken that lessens an undesirable situation or outcome. Because we wish to avoid something undesirable, we engage in behavior that seeks such avoidance. Consider a classroom situation in which students are expected to do their homework every day. If all of the students in the class complete their homework on time for the full week, they do not have to complete a homework assignment on Sunday. In this case, it was a given that students would have to complete the assignment, therefore it was not a punishment (which is something undesirable that is added). Instead, because of a desired behavior, the teacher removes the given thing that is undesirable, in this case, homework over the weekend, making this an example of negative reinforcement. Again, the scenario with the girl playing outside does not seem to be taking away a negative stimulus, so it is not an example of negative reinforcement.
An unconditioned punisher is something that punishes (an undesirable situation that is added) that does not have to be learned. It is something that under most conditions, we would expect someone to naturally want to avoid, such as discomfort or pain. A teacher rapping a students knuckles with a ruler would be an example of an unconditioned punisher, because we would expect any human under normal circumstances to want to avoid that outcome. By contrast, a conditioned punisher is an added undesirable situation that one learns to dislike; a verbal reprimand or stern look might be a conditioned punisher because we are not born knowing what certain words or gestures mean. Instead, we learn to associate them with negative consequences, and they become punishers through socialization. In the case of the girl playing outside, there does not seem to be any punishment per se happening, whether unconditioned or conditioned.
This is why the most likely answer is motivating operations. Motivating operations refer to variables that change the effectiveness of certain stimulus in producing a behavior or effect. The amount that the child is allowed to play outside may increase or decrease the value that playing outside has as a motivating factor for good behavior. If the child is allowed to play all day, then taking away play privileges for an hour does not mean much as a punishment (this is called an abolishing operation, where the value of the motivator decreases). Alternatively, as is often the case in schools, play time outside is often limited to 15–20 minutes for every several hours that the child is inside. This small time frame increases the value of being outside (referred to as an establishing operation, when the value of the motivator increases). Because being outside for the child is a motivating factor in your scenario, and because we see different factors affecting the potential value of that motivator, the best answer is motivating operations.