There seems to be an error in the sequence. However, the result is the same even after this mistake:

>!  $\text{len}(a_{n})$  is the length of $a_{n}$ in English (only letters, no spaces)
>!  
>!  
>!  $a_1 = a_2 = 0$
>!  
>!  $a_n = \text{len}(a_{n-1}) \times \text{len}(a_{n-2})$  for $n \geq 3$
>!  
>!  
>!  $a_1 = 0 \rightarrow$ length of "zero" $\rightarrow \text{len}(a_1) = 4$
>!  
>!  
>!  $a_2 = 0 \rightarrow$ length of "zero" $\rightarrow \text{len}(a_2) = 4$
>!  
>!  
>!  $a_3 = 16 = 4 \times 4 \rightarrow$ length of "sixteen" $\rightarrow \text{len}(a_3) = 7$
>!  
>!  
>!  $a_4 = 28 = 7 \times 4 \rightarrow$ length of "twenty eight" $\rightarrow \text{len}(a_4) = 11$
>!  
>!  
>!  $a_5 = 77 = 11 \times 7 \rightarrow$ length of "seventy seven" $\rightarrow \text{len}(a_5) = 12$
>!  
>!  
>!  Here we have a mistake (or some additional rule that requires you to change from 11 to 12):
>!  
>!  $a_6 = 144 = 12 \times 12 \rightarrow$ length of "one hundred and forty four" $\rightarrow \text{len}(a_6) = 22$
>!  
>!  
>!  But for the correct value we get the same result:
>!  
>!  $a_6 = 132 = 12 \times 11 \rightarrow$ length of "one hundred and thirty two" $\rightarrow \text{len}(a_6) = 22$
>!  
>!  
>!  $a_7 = 264 = 22 \times 12 \rightarrow$ length of "two hundred and sixty four" $\rightarrow \text{len}(a_7) = 22$
>!  
>!  
>!  $a_8 = 484 = 22 \times 22 \rightarrow$ that's the final answer