How many cookies will tanya have if she bakes 6batches more than the maximum number of batches in the table

The number of cookies increases at a constant rate for each batch. The increase is 16 cookies every time. This constant increase represents a linear relationship.

We can form an equation for this linear relationship.
The relationship is in the form  where 

y = number of cookies of 'x' batches
x = number of batches
a = changing rate = 16
b = the number of cookies when the batch is 0

We need to find the value of 'b' and we can achieve this by keep subtracting 16 from 165, which is batch 5 until we get to batch 0.

Batch 5 = 165
Batch 4 = 165 - 16 = 149
Batch 3 = 149 - 16 = 133
Batch 2 = 133 - 16 = 117
Batch 1 = 117 - 16 = 101
Batch 0 = 101 - 16 = 85 ⇒ this is the value of 'b'

So the equation is 

We will use this equation to work out the number of cookies if we cook another 6 batches.

6 batches more than batch 9  will give us batch number 15

We have: x=15, a=16, b=85

y = 16(15) + 85 = 325 cookies