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By Euler formula for connected planar graph,

$\color{red}{n - e + f = 2}$

$n = 14$

$e = 20$

 

$14-20 + f = 2$

$f = 8$

In any planer graph there will be only 1 open region and rest all are closed by edges.

So total closed regions = $8-1 = 7$
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