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So, If my mother who is a 20 handicap decides to play me from the blues, she does not get any extra strokes? Incomplete information for a definitive answer. Making some assumptions from the nature of the way you pased that question, if your Mom is a 20 handicap and so are you, and you both play from the same tees, she gets nada in the stroke department by the rules. Of course, being the mindful and dutiful son that you surely are, you give her strokes just because she's your Mom.

So, If my mother who is a 20 handicap decides to play me from the blues, she does not get any extra strokes?

When talking about a "handicap", what is really meant is a handicap index (HI). I don't have the exact formula on how to calculate it handy, but it's something like 95% of the average HI of the ten best of your last 20 rounds, where the HI is based on an adjusted score (certain per-hole maximums) compared to the course rating, and multiplied by the course slope / 113.

Example: I shoot (an ajusted) 83 [I wish!] on a course with a rating of 69.0 and a slope of 126. My HI for the round is (83 - 69) * (126 / 113) = 15.6

To get the number of strokes allowed for a round based on your handicap, you take your calculated HI multiplied by the course slope / 113. So if the red tees have a slope of 113 and the blue tees have a slope of 139, if your mother's handicap index is 20, then she'd get 4 or 5 (not sure of the rounding rules) extra shots from the blues.