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Well done for giving clear solutions to this problem.  Many of you were able to explain a general strategy.  Tom and Jeevan from Devonshire Primary School said:

If you are trying to make the largest even number using an odd number you put the odd number in the tens column and in the units column you put $8$.
But if you're doing it with an even number then you put $9$ in the tens column and then put the even number in the units column.

Peter, Henry, Charlie, Lulu and Samuel at Weald C of E Primary School assumed that you could also get a zero.  They went on to think about how you would make the smallest even number:

Largest Even
1.If you get an odd number, put an eight in the units column.
2.If you get an even number, put a nine in the tens column.
3.If you get a zero, put a nine in the tens column.

Smallest even
1.If you get an odd number, add a zero in the units column.
2.If you get an even number, add a one in the tens column
3.If you get a zero, put a one in the tens column.
 

Homeroom 7 at Kororoit Creek Primary School, Australia looked at a strategy for making the largest odd number too:

The largest two-digit odd number we could make is $97$. We could not make $99$ because we only have one $9$.
If you pulled out an odd number first this should always go in the 'ones' column. Unless you pull out a number $9$. The $9$ will always go first because $97$ is the biggest number we can make. e.g. $97$, $79$, $59$, $39$, $19$.
If you pull out an even number first it should always go in the 'tens' columns, otherwise your two-digit number will not be odd. You should still always choose the number $9$ as your second card to make the largest number possible. e.g. $89$, $69$, $49$, $29$.  

Well done too to Robert from West Hoathly and Sophie from Greenacre who also sent very full responses.