A piece of wire havi

(i) Since the resistance R is cut into 4 equal parts each part has 1/4^th of the total length. Thus the resistance is 1/4^th the original resistance i.e. each has a resistance of R/4. This is because R is proportional to the length of the wire.
(ii) When the 4 resistances of resistance R/4 each are connected in parallel the equivalent resistance of the circuit is R/16, i.e. it is 1/16^th of the original resistance R.