My dog often licks the palms of my hands. That's how he shows his love for me.
My dog likes to lick the palms of my hands. That's how he expresses his love towards me.
この場合、次のような言い方ができますよ。
ーMy dog often licks the palms of my hands. That's how he shows his love for me.
「私の犬はよく私の掌を舐める。彼の私への愛情表現です」
to lick the palms of one's hands で「掌を舐める」
how he shows his love for me「彼が私のために愛情を表す方法」=「彼の私への愛情表現」
ーMy dog likes to lick the palms of my hands. That's how he expresses his love towards me.
「私の犬は私の掌を舐めるのが好きです。それは彼の私への愛情表現です」
how he expresses his love towards me「彼が私への愛情を表現する方法」=「彼の私への愛情表現」
ご参考まで!