The correct answer is “must”.
“Must” is used to express a strong obligation or necessity. In this case, the speaker is expressing surprise that the listener is leaving so soon after arriving, and is asking them if they really have to go. The listener may have a pressing obligation, such as a job interview or a doctor’s appointment, that requires them to leave early. Or, they may simply be feeling tired or unwell and want to go home. Whatever the reason, the speaker is asking them to confirm that they really have to leave, and is expressing their disappointment that they are going so soon.
The other options are not as appropriate in this context. “Should” is used to express a recommendation or suggestion. In this case, the speaker would be saying that they think the listener should stay, but they are not making it a requirement. “Can” is used to express permission or ability. In this case, the speaker would be asking if the listener is allowed to leave, or if they are physically able to do so. “How” is used to ask about the manner or method of doing something. In this case, the speaker would be asking how the listener is going to leave, or what their plans are for the rest of the day.