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Explanations:

Suppose the man starts from point A travels 15 kms reaches at point B. From point B he turns right and he travels 7 km reaches at point C. From point C he turns right and travels 8 km reaches at point D. From point D again he turns left and travels 3 km reaches at point E. From point E again he turns right and travels a distance of 7 km and reaches at point F. We extend the line ED to touch AB and creates a new point G.

If we draw an image we found we need to find the distance between A and F. AF=EG. EG=ED+DG. DG=BCÂ

=>EG=3+7=10, So AF=10