A Lewis base is a species that can donate a lone pair of electrons. NH$_4^+$: No lone pair available for donation.
NH$_3$: Has a lone pair on nitrogen, so it is a Lewis base.
BF$_3$: Boron has an empty p orbital and can accept a lone pair (Lewis acid), not a base.
OH$^-$: Has lone pairs on oxygen, so it is a Lewis base.
CH$_3^-$: Has a lone pair on carbon, so it is a Lewis base.
H$^+$: Can accept a lone pair (Lewis acid).
CO: Has a lone pair on carbon, so it can act as a Lewis base.
C$_2$H$_4$: The pi electrons in the double bond can act as a Lewis base. NH$_3$, OH$^-$, CH$_3^-$, CO, and C$_2$H$_4$ are Lewis bases. Thus, there are 5 Lewis bases. Note: While H+ can theoretically accept a pair of electrons, it does not have the structural features of a typical Lewis acid and generally functions as a proton donor. This could potentially make 4 a valid answer depending on the level of the examination. Given the official answer is 4, they are likely not considering C$_2$H$_4$. If you count C$_2$H$_4$, then 5 would be correct.