In the second part of this talk, we shall continue from the end of last time; namely understanding wall-chamber structure for the Atiyah flop/ blowing up two general points in $\mathbb{P}^{3}$ and a sextic del Pezzo surface in the language of toric geometry. Next, we shall recall the Hilbert-Mumford criterion for detecting GIT (semi)stable points, focusing on the toric case of understanding the weight polytope. Using this, we sketch the main wall-crossing theorem for topic GIT quotients (in the sense of Thaddeus and Dolgachev-Hu) and extrapolate the analysis to the general setup. Next, if time permits or in the third part of the talk, we shall use the above background to discuss logarithmic Hilbert scheme (in the sense of Siebert-\'et al) of points and wall crossings for certain degenerations of logarithmic Hilbert scheme of points.