I have at my disposal I, I6, V and V7 and inversions as well as ii, ii6 and IV to harmonize this melody. I am also allowed to use the cadential 64. I am stuck on the beginning part on how to harmonize ^2 to ^4. I could use the cadential 64 on the first beat of bar 2 but I think that, given the bass notes below, the cadential V is on beat 3 of the second bar. That is why I began bar 2 with I moving to ii6. The reason I am stuck at the beginning is because if the ^4 is part of a V7 then having a subdominant chord for the 1st chord wont work because the 7th wont be prepared. Am I right then in saying that the only option I have then is to harmonize the first 2 chords with V7 chords or inversions? That way the 7th would be transferred from an inner voice in the 1st chord to the soprano in the 2nd chord.
In addition to your 2–4–3 in the soprano, I would include the next scale-degree 2, as well. This way, a 2–4–3–2 soprano line could be harmonized with voice exchanges in contrary motion in the bass to prolong ii.
The 2–4 in the soprano could be harmonized with 4–2 in the bass, moving from a ii6 to a ii. Then, the 4–3–2 in the soprano could be harmonized with a 2–3–4 in the bass, ending back on your prior ii6.
As for the scale-degree 3, remember that inversions of tonic can prolong predominant chords. Thus, in your progression from ii to ii6, you can insert a I6 that functions as a passing chord to prolong predominant.
All of this, of course, will smoothly move to the cadential six-four on beat 3 of the second measure.