Your answer depends on your question and methodology. If you're conducting an overview, 4-6 could be acceptable (e.g., a qualitative literature review). If you're using PRISMA and want to be comprehensive, every study should be included (common to see 20-50, but could be much higher). PRISMA can help you be systematic.

Timulak, L. (2009). Meta-analysis of qualitative studies: A tool for reviewing qualitative research findings in psychotherapy. Psychotherapy Research, 19(4-5), 591-600.

Timulak, L. (2014). Qualitative meta-analysis. The SAGE handbook of qualitative data analysis, 481-495.

It also depends on how well researched is your topic. If you are researching an area that is not well researched you may struggle to get studies to include in your evidence synthesis.

The premise to work from is that in order to conduct a systematic review/meta analysis or evidence synthesis you should have 2 or 3 papers. If you can't get at least 2 papers on a topic then you would not be able to conduct a review/synthesis. On the other hand it is not advisable to curb your literature to a certain minimum, you should include everything you find (based on your methodology). If you decide to place a minimum number and decide to stop when you reach it, you are likely miss important findings that would have given you a totally different outcome on your research question.

In summary, make sure you can find more than 1 study in order to conduct a review, and based on your methodology use all the eligible studies that you find.

There is no absolute number (minimum count) of case-based (published) studies for conducting meta-synthesis, however, count of 5-8 prior studies can be considered as an appropriate sample further depending on the developmental stage of the area/topic.