Answer
Bronsted-Lowry acid: $H_{2}O$
Bronsted-Lowry base: $CH_3NH_2$
Conjugate acid: $CH_3NH_3^+$
Conjugate base: $OH^{-}$
Work Step by Step
According to the Bronsted-Lowry definition,
Acid: proton ($H^{+}$ ion) donor
Base: proton ($H^{+}$ ion) acceptor
In the reaction, $H_{2}O$ is the acid because it donates a proton to water.
$CH_3NH_2$ is the base because it accepts the proton.
A conjugate acid is any base to which a proton has been added. So, $CH_3NH_3^+$ is the conjugate acid.
A conjugate base is an acid from which a proton has been removed. So, $OH^-$ is the conjugate base.
