Electrical hook up for new stove top
You can keep the existing wiring and breaker
Range loads are computed from their wattage, based on the rules in NEC's Table 220.55.  In particular, since 422.10(A) paragraph 4 explicitly permits range loads to be sized as per Table 220.55:

Branch circuits and branch-circuit conductors for household
ranges and cooking appliances shall be permitted to be in
accordance with Table 220.55 and shall be sized in accordance
with 210.19(A)(3).

we can then apply the logic from Note 4 to Table 220.55 to our situation:


Branch-Circuit Load. It shall be permissible to calculate the branch-circuit load for one range in accordance with Table 220.55. The branch-circuit
load for one wall-mounted oven or one counter-mounted cooking unit shall be the nameplate rating of the appliance. The branch-circuit load for a
counter-mounted cooking unit and not more than two wall-mounted ovens, all supplied from a single branch circuit and located in the same room,
shall be calculated by adding the nameplate rating of the individual appliances and treating this total as equivalent to one range.


In our case, given that we have a 6.4kW, 240V cooktop, we treat this as the branch-circuit size, without derating, giving us something in the 27A range.  As a  result, since we're below the 8.75kW threshold set by NEC 210.19(A)(3), we can use that as our branch circuit load, giving us a 30A branch circuit and breaker with 10AWG wire.  Since it's a 220-240V appliance and not a 110/220 or 120/240V one, we also know that it has no use for a neutral, which means that's not a concern when wiring this, either.  In your case, since you are dealing with a conduit run for the existing branch circuit, the new cooktop needs to be wired the same way the old one was: black to black, red to red, and green to the box, with the white wire in the box left capped off as it is right now.