These metrics are measured through the number of times a publication is cited. Citation metrics include the h-index, citation counts through Scopus, impact factors, and SciVal to count citations over time.
H-index: what it is and how it is calculated
The author in this example has a h-index of 8, because they have 8 papers that have been cited more that 8 times. They do not have an h-index of 9 because the 9th paper was only cited 8 times.
The h-index is defined as the maximum value of h such that the given author/journal has published h papers that have each been cited at least h times. The index is designed to improve upon simpler measures such as the total number of citations or publications. The index works properly only for comparing scientists working in the same field; citation conventions differ widely among different fields.