解:集合\(A=\left \{ {{x|{x}^{2}-3x+2=0}} \right \} =\left \{ {{1,2}} \right \} \),\(B=\left \{ {x|0<x<6,x∈\text{N}} \right \} =\left \{ {1,2,3,4,5} \right \} \),
∴满足\(A⊆C⊆B\)的集合\(C\)有:{1,2},{1,2,3},{1,2,4},{1,2,5},{1,2,3,4},{1,2,3,5},{1,2,4,5},{1,2,3,4,5},共8个.故选:B.