cumulative distr. $X,Y$ independent what is wrong here? ($X,Y$ are independent):
$1 - P(X > u, Y >u)  = 1 - (1 - P(X \leq u, Y \leq u)) =1 - (1 - F_X(u)F_Y(u)) $.
it should say, in the last equality:$  = 1 - (1 - F_X(u)) (1 - F_Y(u)) $ what am I missing/ doing wrong?
 A: The second step is wrong. You say:
$$1- P(X>u,Y>u) = 1- (1-P(X\leq u, Y\leq u))$$
which is equivalent to saying:
$$P(X>u,Y>u)=1-P(X\leq u, Y\leq u)$$
which is not true.
What you should have is:
$$P(X>u,Y>u)=1-P(X\leq u \mbox{ or } Y\leq u).$$
Maybe it helps to write: $A:=\{X>u\}$, $B:=\{Y>u\}$ where the events $A$ and $B$ are independent: Then
$$P(A\cap B) = 1- P((A\cap B)^c) = 1- P(A^c \cup B^c)$$
and for two given events $A$ and $B$ one has:
$$P(A \cup B) = P(A) + P(B) - P(A\cap B)$$
A: It has already been explained that your first inequality is not right. In general,
$$1 - \Pr(X > u, Y >u)  \ne 1 - (1 - \Pr(X \leq u, Y \leq u)).$$
Informally, this is because $X\gt u, Y\gt u)$ and $X\le u,Y\le u$ do not exhaust all possibilities: We could have $X\gt u$ but $Y\le u$. 
Additionally, there is a typo in your second equality. The $1-F_X(u)$ is right, but it should be multiplied by  $1-F_Y(u)$. 
The actual solution is quick: 
Note that $\Pr(X\gt u)=1-F_X(u)$ and $\Pr(Y\gt u)=1-F_Y(u)$. so by independence we have
$$\Pr(X\gt u,Y\gt u)=(1-F_X(u))(1-F_Y(u)),$$ which gives you the desired result. 
