How to realize DFT6 with 3 DFT2 blocks?
The following is an important paper about FFT algorithms:

Tran-Thong, “Algebraic Formulation of the Fast Fourier Transform,” IEEE Circuits and
Systems magazine, vol. 3, no. 2, June 1981, pp. 9-19.

In the above, the author distinguishes 16 basic types of FFT algorithm, characterized by: 1) decimation type (DIT - type T below, or DIF - type F below), 2) input order, 3) output order, and 4) geometry.  The author also shows graphs, but they will not be shown here.

Alg.    Input Order Output Order Geometry

T1      bit reverse sequential  in-place
T2      sequential  bit reverse in-place
T3      bit reverse bit reverse same output
T4      sequential  sequential  same output
T5      bit reverse bit reverse same input
T6      sequential  sequential  same input
T7      bit reverse sequential  isogeometric
T8      sequential  bit reverse isogeometric

F1      bit reverse sequential  in-place        
F2      sequential  bit reverse in-place
F3      bit reverse bit reverse same output
F4      sequential  sequential  same output
F5      bit reverse bit reverse same input
F6      sequential  sequential  same input
F7      bit reverse sequential  isogeometric
F8      sequential  bit reverse isogeometric


Although many of the algorithms can be attributed to different authors, as stated in the above paper: "The Cooley-Tukey algorithm and its modifications are DIT algorithms.  The Gentleman-Sande algorithms and their modifications are DIF algorithms."

There are many more FFT algorithms other than the ones described above, including higher and mixed radix ones.  But they also exhibit similar characteristics.  For instance, take a look at the 6 point DIT radix-3/radix-2 graph shown on page 13 in the following reference:

http://www.ece.cmu.edu/~ee791/lectures/L18/FFTstructures.pdf

It is two radix-3 butterflies followed by three radix-2 butterflies.  It is bit-reversed input and sequential output.

Of course, given that the FFT can be viewed as a matrix transpose, one can also decompose a 6 point FFT into three radix-2 butterflies, followed by two radix-3 butterflies.  You can also have DIT or DIT (or mixed decimation).  So you have several options to choose from.