Certainly! The image asks you to convert the binary number 110110011_2 to its equivalent in base 8 (octal).

Step-by-Step Solution:

1. Group the binary digits into sets of three (starting from the right):

   • 110 110 011

2. Convert each group to its decimal (base 10) equivalent:

   • 110 in binary is 6 in decimal.
   • 110 in binary is 6 in decimal.
   • 011 in binary is 3 in decimal.

3. Write the decimal numbers together to get the base 8 (octal) equivalent:

   • The base 8 equivalent of 110110011_2 is 663_8.

So, the correct answer is $\boxed{663}$.

Would you like further details or have any questions? Here are some related questions:

1. How do you convert a binary number directly to a hexadecimal number?
2. What is the method for converting a decimal number to a binary number?
3. Can you convert the binary number 101010_2 to octal?
4. How would you convert the octal number 764_8 to binary?
5. What is the significance of the base in numeral systems?

Tip: When converting binary to octal, grouping the binary digits in sets of three from the right makes the process straightforward, as each group corresponds to a single octal digit.