Answer
The value of $F$ is $9.73N$.
Work Step by Step
To be able to solve the problem, we need to translate $F$ into $x$ and $y$ components. To do so, we need to find the angle $\vec{F}$ makes with the horizontal, $\theta$, first.
In the photo (a) below, we see that in this exercise, $\theta=45^o$.
1) The horizontal forces
From photo (b) below, it is clear that 2 horizontal forces $F\cos\theta$ cancel out each other. So, the net force here is $0$.
2) The vertical forces
From photo (b), if we take the direction of 2 $\vec{F}\sin\theta$ forces to be $+y$ direction, then $m\vec{g}$ is in $-y$ direction. As the bottle stays still vertically, these forces balance each other, too.
$$mg=2F\sin\theta=2F\sin45$$ $$1.4\times9.8=1.41F$$ $$F=9.73N$$
