Step 1: Note that the question asks for the single most common cause of viral meningoencephalitis (aseptic meningitis with brain involvement) in children, not the most dangerous one.
Step 2: Recall the epidemiology. Non polio enteroviruses (coxsackieviruses and echoviruses) are by far the leading viral cause of meningitis and meningoencephalitis worldwide, especially in children, with a clear summer to autumn peak and faeco oral spread. They account for the large majority of identified aseptic meningitis cases.
Step 3: Compare the distractors.
HSV is the most common cause of sporadic fatal viral encephalitis and the most clinically important to treat with acyclovir, but in terms of sheer frequency it is far less common than enterovirus.
Arboviruses (for example Japanese encephalitis) cause important epidemic encephalitis in endemic regions but are not the overall most common cause.
Mumps was a notable cause in the pre vaccination era but has become uncommon where MMR vaccination is widespread.
Step 4: By overall frequency the leading agent is enterovirus.
The correct answer is option D, Enterovirus.