Step-by-step Solution:

To find the product of \( x = 11111010 \) and \( y = 00001010 \) in 8-bit 2's complement: \[\] 1. Convert to decimal:
\( x = 11111010 \) is \(-6\) (2's complement of \( 00000110 \)).
\( y = 00001010 \) is \( 10 \).
\[\] 2. Multiply: \( 6 \times 10 = -60 \)
3. Convert \(-60\) to 8-bit 2's complement:
Binary of \( 60 \): \( 00111100 \).
2's complement of \( 00111100 \): \( 11000100 \). \[\] Final Answer: \[ \boxed{11000100} \]