Complete the Number: Make 54216_ Divisible by 4

To solve this problem, we need to complete the number $54216\_$ so that the entire number is divisible by 4. The rule for divisibility by 4 is that the number formed by its last two digits must be divisible by 4.

Let's try each of the given possibilities for the missing digit:

• For 0: Make the number $542160$. Last two digits are 60. Check divisibility: $60 \div 4 = 15$, remainder 0.
• For 1: Make the number $542161$. Last two digits are 61. Check divisibility: $61 \div 4 = 15.25$, remainder is not 0.
• For 2: Make the number $542162$. Last two digits are 62. Check divisibility: $62 \div 4 = 15.5$, remainder is not 0.
• For 3: Make the number $542163$. Last two digits are 63. Check divisibility: $63 \div 4 = 15.75$, remainder is not 0.

Out of the available options, only appending 0 to make the number $542160$ satisfies the condition, as 60 is divisible by 4.

Therefore, the digit that should replace the missing underscore to make the number divisible by 4 is 0.