I came across the sentence like
"The ship began to move gently down the river with the out-running tide".
I checked "out-running tide" in dictionary but I can't find them. Could you teach me?
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The out-running tide is tide which is running out. The participle-phrase can be turned into an adjective, but when that happens, the preposition, here out, is moved to the head:
When the tide is running out we can call it the out-running tide.
You won't necessarily find in a dictionary every adjective which can be formed in this manner.
Although it would be grammatical to transform almost any such phrase in this manner, if native speakers as a group don't tend to do so, the transformation would sound a little odd, or perhaps "literary". Here's an example:
His baggy trousers were slipping down.
He tightened his belt because he was wearing baggy down-slipping trousers.
All you have know is what the definition of 'tide' is. Basically it's the local sea level of the ocean that gets influenced every 6 hours or so by the orbits of the sun and the moon. Tide tables are published that forecast what that's gonna be. "Running with the tide" (in or out) means going with the flow of whatever everybody else is doing. There's a grammar term for that, but it's really not important. Just understand "out-running tide" means the water flow is running out (water level flowing out, water going to get lower). Opposite is tide "running in" (water level flowing in, water going to get higher).