This story is an example of an outright hoax.
There are a number of sources of the story. Here is one version.
We have come across many reports regarding earth and its changes in recent times and not many materialize. However, this time NASA has confirmed that earth will experience total darkness for 15 days in November 2016 starting from November 15 to November 29.
Of course, NASA has said no such thing. And it occurred to me that for someone living in the far north, this would just be business-as-usual for the time of year. In Hammerfest, Norway, the Sun will set on the morning of the 19th and not rise again until the 22nd of January.
But really, this general darkness thing isn't going to happen. The explanations of it seem to vary from site to site, but all of them are ridiculous. Fortunately, you don't have to take my word for it. Today is November 13th, so you don't have long to wait to see for yourself.