I understand that $1$ word is $4$ bytes in the $32$bit address system, so the byte offset is $2,$ but I wonder what happens in $64$bit address and please solve the problem.

Compute the sizes of the tag bits and the index bits.

$($a$)$

direct mapped

$64$ KB of data with $4-$word blocks

$32-$bit address

$($b$)$

$4$ way set associative

$64$ KB of data with $8-$word blocks

$64-$bit address

$($c$)$

fully associative

$256$ KB of data with $16-$word blocks

$64-$bit address