How do scientist determine where an earthquake starts?

They use seismology

Explanation:

Seismology is the study of seismic shocks (earthquakes), in order to understand and determine the mechanisms involved in the plate tectonics of our planet, as well as their causes and distribution over the terrestrial globe, in an attempt to predict them in time and space at from the analysis of circumstances in which natural earthquakes occur. As a method of geophysical study, seismology also performs analyzes on the structure and layers of the Earth, from its surface to the nucleus.

Through seismology, seismic waves emitted by earthquakes can be detected, recorded and analyzed. From this analysis, information can be obtained about the precise location of the earthquake (epicenter), its depth, released energy, the mechanism that generates the shock, and the means that the waves traveled to reach the place where they were generated until the sensor that detected them.