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Please refer to the picture below:

This is just a problem about similar triangles. So we know that:
Because they share common sides then they are similar so:
 \frac{AC}{AE} = \frac{BC}{DE} = \frac{15}{6} = \frac{5}{2}
We let CE be x then this would make:
 \frac{20+x}{20} = \frac{5}{2}  \\ (20+x)2=5*20 \\ 40+2x=100 \\ 2x=60 \\ x=30

Therefore the man should stand 30 feet from the light to cast a shadow of 20ft long.

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