What is there is one that has a head without an eye And there's one with an eye without a head. you may find the answer if you try And when all is said half of the answer upon a thread?

The riddle describes two objects: a needle (which has a "head" but no eye) and a potato (which has an "eye" but no head). The phrase "half of the answer upon a thread" suggests that the answer relates to sewing, where a needle is used with thread. Therefore, the answer is "needle and potato."