How many ways are there of choosing the first ball? It could be any one of the 36 original balls, so the answer is 36.
Once that ball is out of the mix, how many ways of choosing the second ball? Well, there are no longer 36 balls in the supply; there is one fewer, so the answer is 35.
Multiply these two numbers together to find the number of different ways of choosing two different balls from the supply, with the order being significant.
Carry on multiplying (not forgetting to remove the ball you chose from the number of remaining balls) until you have selected the 6 balls.
You will have quite a big number. This is the number of different ways of choosing a sequence of 6 balls in order from a stock of 36, without repetitions.
Given that in your question the order seems to be important, this is your answer. However, for many lotteries, you wouldn't have finished yet.
For most lotteries, the order the balls were selected in is not important. You could have selected the balls in any order and the result would have been effectively the same. So you have counted all these combinations too often: 1, 2, 3, 4, 5, 6 is effectively the same as 1, 2, 3, 4, 6, 5 for example.
How many times have you counted each combination of balls? (A combination is a set of objects where the sequence the objects appear in is not important)
Well, any of the 6 balls could have been in first place, and any of the 5 remaining could have been in second.
$6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$
So for each sequence without repetition, there are $720$ ways of writing it down in a different order. So divide the number of sequences by $720$ and you'll get the number of combinations of 6 balls from a stock of 36.