To determine the Lewis structure you must know which are the valence electrons of the elements that make up the molecule. In this case it is boron and fluorine.
Boron is in group 3, so it has 3 valence electrons. Fluorine is in group 7, so it has 7 valence electrons. Fluorine needs one electron to satisfy the octet rule and boron needs 5 electrons to satisfy the octet rule.
Remember that in the Lewis structure the dots represent the electrons and the lines represent the bonds formed by a pair of electrons.
We can discard the options that show boron with more than 8 electrons.
In option A, boron has 4 bonds (8 electrons) and two additional electrons, in total 10 electrons.
In option B, boron has 5 bonds (10 electrons)