An example of a real-world externality is the use of fossil fuels. The use of fossil fuels creates pollution, which leads to global warming. A possible solution to this problem is to tax the use of fossil fuels. This would discourage the use of fossil fuels and lead to a more efficient allocation of resources.
An example of a real-world public good is a lighthouse. A lighthouse provides a benefit to everyone in the area, regardless of whether they contributed to the construction of the lighthouse or not. A possible solution to this problem is to charge people (Gächter et. al. 2017).
I am currently facing a negative externality in my neighborhood. There is a new factory that has opened in my neighborhood and the air quality in the surrounding environment has rapidly started to deteriorate. The problem of the situation is that the habitants of the neighborhood are facing poor quality of air to breathe.
References
Gächter, S., Mengel, F., Tsakas, E. and Vostroknutov, A., 2017. Growth and inequality in public good provision. Journal of Public Economics, 150, pp.1-13.