This is the 9177th most frequent Japanese word.
片手
"片手" means "one hand" or "one-handed."
In this sentence, '片手' (katate) refers to 'one hand,' indicating the use of one hand to perform the action of throwing the ball.
彼は片手でボールを投げた。
He threw the ball with one hand.
Here, '片手' is used to describe the condition of holding a smartphone in one hand while performing another action, walking.
片手にスマートフォンを持ちながら歩いている人がいる。
There are people walking while holding a smartphone in one hand.
In this sentence, '片手' is indicating the use of only one hand to perform the activity of carrying luggage, discussing the difficulty of doing so.