The correct option is A B(NH2)3<B(OH)3<BF3<BCl3
Lewis acid - Tendency of a species to accept an electron pair in its empty orbital.
Firs,t check overlapping with the side atom which can donate a pair of electrons
BCl3 overlapping is 2p-3p
B(NH2)3 overlapping is 2p-2p
B(OH)3 overlapping is 2p-2p
B(F)3 overlapping is 2p-2p
bond strength 2p-2p>2p-3p, empty orbital of B in BCl3 has a high tendency of accepting a pair of electrons from a lewis base.
B(OH)3, B(NH2)3 and BF3 have same overlapping strength so let's check the electronegativety of the side atom. If the electronegativety of the side atom is high, then the lewis acidic strength of that species will be greater than the others. Among B(OH)3, B(NH2)3 and BF3, the lewis acidic strength is
B(NH2)3<B(OH)3<BF3<BCl3