Firstly you copied the wrong sequence,
It ought to be 2, 6, 8, 54, .... there is no 16.
The formula is = 2 × 3ⁿ, n = 0, 1, 2, 3, 4, ....
The next term, n= 4
2 × 3⁴ = 2 × 3× 3× 3× 3 = 162
That is how she got 162. So the formula she is using is:
2 × 3ⁿ, n = 0, 1, 2, 3, 4, 5, 6,....
