The 7th term of an AP is 12 and its 12th term is 7…

Step 1. Two equations. $a + 6d = 12$ and $a + 11d = 7$.

Step 2. Subtract. $5d = -5$, so $d = -1$ and $a = 18$.

Step 3. The $19$th term. $a_{19} = 18 - 18 = 0$.

Step 4. In general. $a + (p - 1)d = q$ and $a + (q - 1)d = p$. Subtracting gives $d = -1$, so $a = p + q - 1$. Then $a_{p+q} = (p + q - 1) - (p + q - 1) = 0$.