You mean the image location on the child's retina? To get that you'd have to know the focal length of the child's eye at 20 cm. Call it f. Then

1/f = 1/p + 1/q, p = 20cm and solve for q.

If you wanted the size of the image on the child's retina it would be 8cm*(q/p).

I must be missing something here ....?

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