Hiyas ThisAintRight2,
I will always add a timezone converter website in my promos I post, so it will be easier to figure out the timezone changes for everyone. As unavailable stated, however, Local Server Time in a post always means the server time for the version you play on (i.e. CEST = Central Euro time for European servers and EST = Easter time US server). I add both as English posts are for both our UK players on Elysion/Atlas/Inferna and US players on NA servers.
Sometimes Promos are only set in Local Server Time (like weekly sales). This means they start at XX:xx Local server time for each versions separately (i.e. EST for US, MSK for RU and EU for DE, FR, PL, ES/IT and EU).
Sometimes Promos are only set up to run in CEST time and not local server time. Those will simply have XX:xx CEST (XX:xx EST) as the promo begins at the same set time for all versions equally.
As Mendek stated, there are programs which can help. I, personally, use Widgets on my PC and have 3 clocks on my deskstop. One for EST, one for CEST and one for MSK as I run versions in each of those timezones.