This is one of those questions that trips people up more than it should. The numbers feel like they're hinting at something obvious, but the obvious answer is wrong.
Most people say 8. A few say 4.
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Solution:
The actual answer is 16, and here's why:
Start with what you're actually given: four men finish four tables in four hours. That's one table per man in four hours. Simple enough. Each man's rate is 1 table per 4 hours, or 0.25 tables per hour.
Now double the time. Eight hours instead of four. Each man now completes 2 tables since he's working twice as long.
Finally, double the workers. Eight men, each building 2 tables, gives you 16 tables total.
The trick is that the question doubles both the time and the workforce. People who answer 8 usually double only one variable in their head without realizing it.
This kind of problem is a basic example of proportional reasoning. It shows up in real planning too. If you're estimating how long a project takes with a bigger team and more hours, the same logic applies. Scale both dimensions correctly or your estimate will be off.
The moral of the problem? Don't rush. Read the numbers twice. Doubling everything isn't the same as changing nothing.