Find an hour that works for everybody

Put your zones on one strip and read the overlap directly. Working hours are shaded, so the answer is a band you can choose from rather than a single time you have to verify person by person.

Converting one time at a time hides the answer

The usual approach is to guess a time, convert it for each participant, discover it is 6am for one of them, and guess again. Drawing the zones side by side turns that loop into a glance: the overlap is visible, and so is the fact that some sets of zones have no civilised overlap at all.

It tells you when there is no good answer

Some combinations genuinely have no hour that is reasonable for everyone — California and India is the classic. Seeing that immediately is more useful than finding it out after four rounds of suggestions, because it changes the question from "when" to "who records it".

Questions

Why does the difference between two time zones change during the year?

Because countries change their clocks on different dates. The United States moves in March and November, the European Union in the last weekends of March and October, and the southern hemisphere moves the opposite way entirely. For a few weeks each year the usual gap is an hour out, which is when most mis-scheduled calls happen.

What does CST actually mean?

It depends who wrote it, and that is the problem. CST is US Central Time and it is also China Standard Time — fourteen hours apart. IST is India, Ireland and Israel. Every conversion page here names the zone it resolved an abbreviation to, rather than quietly picking one.