A random variable following a binomial distribution over trials with success probability has PMF
Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.
The mean is given by the expected value of the distribution,
The remaining sum has a summand which is the PMF of yet another binomial distribution with trials and the same success probability, so the sum is 1 and you're left with
You can similarly derive the variance by computing , but I'll leave that as an exercise for you. You would find that , so the variance here would be
The standard deviation is just the square root of the variance, which is
I like to solve these by graphing, so if you graph both of these functions (as shown in the picture below), you look for the intersection between the two graphs, which in this case is (-2,6).