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

Synthesizing $2h/e^2$ resistance plateau at the first Landau level confined in a quantum point contact