Is this fixed length MAC unforgeable?
Forgeries can be made against this algorithm; here's how:

If the attacker gets the MAC with the two messages M0||M2 and M1||M3 as follows:

MAC(M0||M2) = Fk(0||M0) || Fk(1||M2)
MAC(M1||M3) = Fk(0||M1) || Fk(1||M3)


then, the attacker knows the values of Fk(0||M1) and Fk(1||M2), and thus can deduce the MAC of the message M1||M2 as:

MAC(M1||M2) = Fk(0||M1) || Fk(1||M2)


BTW: is this a homework assignment?