打
dǎ
One verb, one reaching hand: 打
The picture A hand shooting out and tapping something, and the thing starts happening. 打 reaches out until it touches; 拿 closes on what it touched and brings it back to you.
Where the picture shows up in 打
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tap the line
我一会儿打电话给你。
wǒ yíhuìr dǎ diànhuà gěi nǐ
I'll call you in a bit.
A fingertip tapping the keypad, and across town a phone starts ringing
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grab it out of the air
太晚了，我们打车回去吧。
tài wǎn le, wǒmen dǎchē huíqù ba
It's late — let's take a cab back.
An arm shooting up at the curb and a passing taxi pulling over
打车 pictures your hand going up to flag a car. Once you're sitting in one, it's 坐车.
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wrap it up in your hands
剩下的帮我打包一下。
shèngxià de bāng wǒ dǎbāo yíxià
Could you box up the leftovers?
Leftovers swept into a box, both hands pressing the lid shut
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strike it onto paper
这份合同请打印两份。
zhè fèn hétong qǐng dǎyìn liǎng fèn
Please print two copies of this contract.
Type striking paper again and again, letters left behind where it hit
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jab it in
医生说要打一针。
yīshēng shuō yào dǎ yì zhēn
The doctor says I need a shot.
A needle tapping into the upper arm and the medicine going in
All of it in one picture
打 is one hand reaching out. Fingertips touch the keypad and it is a phone call; the hand goes up and catches a taxi; both hands close around the food and it is a takeout box. Type strikes the paper and it is printing; the needle strikes the arm and it is a shot. So wherever 打 turns up, look for the hand going out, making contact, and the business starting from that contact.