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You can work this out pretty quick; just assemble the number in parts. We know the number must be odd, so the last digit has to be an odd one. Let's make it three:

3

Now we need to add five more digits that collectively add up to seven (giving us the sum of ten for our six digits. There's no limit of repetition limit, so we can simply say our numbers are 1, 1, 1, 2 and 2:

111223

That's our last six digits that add up to ten. To get four different eight-digit odd numbers, all we have to do is add four combinations of two digits on the beginning:

99111223

98111223

97111223

96111223

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Q: What is four eight-digit odd numbers whose last six digits have the sum of ten?
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