What is the last nuclear reaction in a binary system before supernova?

I guess it depends on the type of Supernovae.

Type 1a supernovae are produced by a white dwarf star orbiting a companion close enough that matter transfers from the companion to the surface of the white dwarf.

Assuming only your star system of a 3M star and 6M star, the 6M star would become a white dwarf star first. At the end of it's life, it would have been furiously converting hydrogen to helium, and helium to carbon via the C-N-O cycle and the triple alpha process (C-N-O being dominant in stars above 1.3M sol). The highest reaction in this stars main sequence lifetime would have been the creation of oxygen, but oxygen is a catalyst in the C-N-O cycle, and therefore the last probable reaction in the star would be that of Helium in some form of shell burning in the outer core (more on that next).

The white dwarf, while orbting the companion, may siphon off hydrogen from the surface of the donor star. This hydrogen will accumulate evenly over the surface of the dwarf star, slowly growing the mass of the dwarf. Also, the hydrogen will be shell-burned into helium during this time increasing the density.

If sufficient mass can be accumulated, then the carbon within the white dwarf can ignite in a runaway reaction - literally blowing the entire star apart. These supernovae produce every element up to Nickel (Ni-56).