Multiplication of 478 by 528 is A. (3144)8 B. (4147)8 C. (3146)8 D. (3184)8 E. None of the above

The correct answer is $\boxed{\text{(3146)}_8}$.

To multiply 478 by 528 in base 8, we can use the following algorithm:

1. Write the numbers in columns, with the larger number on top.
2. Starting from the right, multiply each digit in the bottom row by each digit in the top row, and write the product in the corresponding column of the answer.
3. If the product of two digits is greater than 7, carry the 1 over to the next column.
4. Continue multiplying until you reach the bottom of the bottom row.
5. Add up the digits in each column of the answer, carrying over any extra digits to the next column.

The product of 478 and 528 in base 8 is:

$$\begin{array}{cc|cc}
\multicolumn{2}{r}{4} & 7 & 8 \
\cline{2-4}
5 & 2 & 8 & 0 \
\multicolumn{2}{r}{4} & 7 & 8 \
\cline{2-4}
3 & 1 & 4 & 6
\end{array}$$

Therefore, the answer is $\boxed{\text{(3146)}_8}$.

Here is a brief explanation of each option:

• Option A: $\boxed{\text{(3144)}_8}$ is incorrect because the product of 478 and 528 in base 8 is 3146, not 3144.
• Option B: $\boxed{\text{(4147)}_8}$ is incorrect because the product of 478 and 528 in base 8 is 3146, not 4147.
• Option C: $\boxed{\text{(3146)}_8}$ is the correct answer.
• Option D: $\boxed{\text{(3184)}_8}$ is incorrect because the product of 478 and 528 in base 8 is 3146, not 3184.
• Option E: $\boxed{\text{None of the above}}$ is incorrect because one of the options is the correct answer.