Suppose, originally there are x machines.
 x machines 1 days work = $ 1/4 $ or 1 machine's 1 day's work  $1/{4x}$ .... (i) 
Also (x + 4) machines 1 days's work = $1/2$
1 machine's 1 day's work = $ 1/ {2(x + 4)} $... (ii)
Equating (i) and (ii),
$ 1/{4x} = 1/ {2(x + 4)} $ or 2x + 8 = 4x
or 2x = 8
or  x = 4
Now, 1 machine's 1 days work = $ 1/{4x4} = 1/16$
2 machine's 1 day's work = $2/16 = 1/8 $
Hence, 2 machines can finish the work in 8 days.