The way of holding something (how to hold an object or tool), e.g. how to hold chopsticks, a brush, or luggage.
箸の持ち方を先生に直してもらった。
My teacher corrected the way I hold chopsticks.
筆の持ち方で字の雰囲気が変わる。
The atmosphere of your handwriting changes depending on how you hold the brush.
重い荷物は持ち方を工夫しないと疲れやすい。
If you don't adjust how you hold heavy luggage, you'll tire easily.
A holder or the person who holds something (similar to 'もちて' / '持ち手'); can refer to the handle or the person in possession.
その箱の持ち方（持ち手）はしっかり作られている。
The handle of that box is well made.
器具ごとに適切な持ち方（人）を決めて作業を始めた。
They decided who would handle each tool and started the work.