Can a 14 inch umbrella fit inside a suitcase that has dimensions of 9" x 12"? explain.

Yes. The umbrella is smaller than the suitcase. The suitcase is 81'^2, but the umbrella is 14

I will assume that when you say 14", you are referring to the diameter of the open umbrella.
When an umbrella is folded down, really the only dimension we need to figure out is the distance from top to bottom - which, when spread open, is the same distance as the radius.
To find the radius: 14 divided by 2 = 7.
No matter which way you turn the umbrella - vertical, horizontal, or diagonal, 7 is smaller than 9 or 12. So yes, you can fit the umbrella in the suitcase when it is closed.

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