I heard Pastor Armstrong teach that Jesus gave up His life at Thursday 6am, but the scriptures states He gave up His spirit at night time. But it also doesn't make sense to be at 3pm because it never gets dark, and the gospels say there was darkness over the land at the time Jesus cried out to God. So what time was it really?
We are unsure which teaching you are referencing, but we do not teach that Jesus died at 6 AM on Thursday. The Scripture is clear that Jesus died at the "ninth hour" (see Luke 23:44-46), which is 3 PM, according to Jewish time.
The time references given in the Gospels are not references to our clock hours but rather to the Jewish and Roman ways of reckoning time. Jews and Romans counted hours in groups of 12, but Jews and Romans counted from different starting points on the clock. It's important to understand this in order to interpret the time references properly.
Here's a helpful chart that compares the way Romans and Jews counted hours on the clock:
Three Gospel writers used the Jewish method of reckoning time (i.e. Luke, John, Matthew), while Mark used the Roman method. When we compare across the four Gospels and make the necessary conversions in time, all four agree: Jesus was crucified at 9 AM, hung on the cross 6 hours until He died at 3 PM, and was removed from the cross and buried before sundown at 6 PM.
So Jesus died at 3 PM on Thursday and was in the grave on that day prior to the Sabbath start at sundown (see Luke 23:53-54). So in counting Jesus' time in the grave, we count Thursday as the first "day" of His three days and three nights in the grave.
For a more detailed examination of the day of Jesus' death, please read: What day of the week did Jesus die?