Looks like 2 incident triangular-hexagonal tilings (that) together with additional coincident triangle pairs, and indeed, vertices and {6} coincide by pairs, edges coincide by 3, and each {3/2} coincides with 3 {3}.

Incidence matrix according to Dynkin symbol

β6β3o   (N → ∞)

both( . . .    ) | 6N |  2  2  2 | 1 1  1  3
-----------------+----+----------+----------
sefa( s6s . (r)) |  2 | 6N  *  * | 1 0  0  1
sefa( s6s . (l)) |  2 |  * 6N  * | 0 1  0  1
sefa( . β3o    ) |  2 |  *  * 6N | 0 0  1  1
-----------------+----+----------+----------
      s6s . (r)  ♦  6 |  6  0  0 | N *  *  *
      s6s . (l)  ♦  6 |  0  6  0 | * N  *  *
      . β3o      ♦  3 |  0  0  3 | * * 2N  *
sefa( β6β3o    ) |  3 |  1  1  1 | * *  * 6N

starting figure: x6x3o