$\left\vert{A \cup B \cup C}\right\vert$

$= \left\vert{A}\right\vert + \left\vert{B}\right\vert + \left\vert{C}\right\vert - ( \left\vert{A \cap B}\right\vert + \left\vert{A \cap C}\right\vert + \left\vert{B \cap C}\right\vert ) + \left\vert{A \cap B \cap C}\right\vert$

$= 4 + 2 + 6 - (1 + 3 + 2) + 1 = 12 - 6 + 1 = 7$