For N = $64$ $bits$.
Suppose you want to build a $64$ $bit$ adder then you need $16$ $4$-$bit$ ALU and $16$ $4$-$bit$ carry generator, at this point there will be $16$ carries that will ripple through these $16$ ALU modules, to speed up the adder we need to get rid of these $16$ rippling carries, now we can again use $4$ $4$-$bit$ carry generator to generate these $16$ carries, now we have only $4$ carries to ripple through, again we can use the same trick to minimize the rippling of these $4$ carries, we can use an additional $4$-$bit$ carry generator which will generate these carry and we are done :) there will be no more propagation of carry among the ALU modules.
So, the we have used $3$ level of $4$-$bit$ carry generator, and the time taken to add $64$ $bits$ will be proportional to $3$ which is log464.
So, in general to add N-bits it takes Log4N time.
Correct Answer: $B$