when MT2 and Gate is Negative
In this case gate current flows through P2N3 junction. Junction N1P2 forward biased hence the triac starts conduction through P1N1P2N2 layer initially. Since the gate is negative with respect to the main terminal but MT1 but MT1 is negative with respect to MT2. Therefore MT1 attracts the holes from P2 layer through N2 layer and triac starts conducting through P1N1P2N2 layer.
Figure When MT2 is positive and g is negative