Help with a variance proof

Question

I've been doing these exercises, but there is a proof (considering a binomial distribution of $n=4$, where $p$ is the probability of something happening, that has a median $m=4p$, prove, using the summation of $x_ip_i-m^2$, that the variance is $4p(1-p)$) that didn't work out. Pls help, as it is a special case and I cannot find anything relevant.