$\large \exists x \forall y R(x,y) \ \text{IMPLIES} \ \forall y \exists x R(x,y) $
$\large \exists x \forall y R(x,y) \rightarrow \forall y \exists x R(x,y) $
let $R(x,y)$ be be $\text{x and y are friends}$
$\large \exists x \forall y R(x,y)$ means there is an x for which R(x,y) is true for every y.
which also means "there exists x which is friends with every y"
$\large \forall y \exists x R(x,y) $ means for every y there is a x for which R(x,y) is true
which also means "for every y there exist some x such that x and y are friends"
So if premise,$(\large \exists x \forall y R(x,y))$ is true,
then conclusion can never be false because for making conclusion as false there must exist a y which doesn't have any x to be friends with but premise told us there is an x for every y.
Hence Valid
