Value of a

The number $3^{19}$ is divisible by $3^2=9$ . The simple check for divisibility with $9$ is to verify the divisibility of the sum of digits with $9$ . Therefore, $1+1+a+2+2+6+1+4+6+7$ should be a multiple of $9$ . On simplifying: $30+a$ should be a multiple of $9$ . Since $a$ is a single digit here, it has to be $6$ .