Recall that if $G$ is a connected planar graph with $v\geq 3$ vertices and $e$ edges then we always have
That means, in this case, we need an example of which equality holds in the above inequality.
Let us draw such an example by taking $v=3$. Note that in this case $3v-6=3$. Now we have to create a graph on three vertices such that the number of edges in it is three. So the graph is nothing but a triangle.