2024 ACS(BR) P2 Q1

A particle moves along the curve \(y=\dfrac{3(x+6)}{x+4}\), where \(x\ne-4\), in such a way that the \(y\)-coordinate of the particle is increasing at a constant rate of \(\dfrac4{27}\) units per second. Find the \(x\)-coordinates of the particle at the instant that the \(x\)-coordinate of the particle is decreasing at a rate of \(2\) units per second.[5]