A comprehensive understanding of quantum Hall edge transmission, especially a hole-conjugate of a Laughlin state such as a 2/3 state, is critical for advancing fundamental quantum Hall physics and enhancing the design of quantum Hall edge interferometry. In this study, we report a robust intermediate 2h/e 2 resistance quantization in a quantum point contact (QPC) when the bulk is set at the fractional filling 2/3 quantum Hall state. Our results suggest the occurrence of two equilibration processes. First, the co-propagating 1/3 edges moving along a soft QPC arm confining potential fully equilibrate and act as a single 2/3 edge mode. Second, the 2/3 edge mode is further equilibrated with an integer 1 edge mode formed in the QPC. The complete mixing between them results in a diagonal resistance value quantized at 2h/e 2 . Similar processes occur for a bulk filling 5/3, leading to an intermediate (2/3)h/e 2 resistance quantization.