Solve the following equation for x: 3 times 125x equals two-third of 2100.

"Three times $125x$" can be written as $3 \times 125x$.
"Equals" means $=$.
"Two-third of 2100" can be written as $\frac{2}{3} \times 2100$.
So the equation is:

$$3 \times 125x = \frac{2}{3} \times 2100$$

Multiply on the left side:

$$375x = \frac{2}{3} \times 2100$$

Calculate the right side:

$$375x = 2 \times \frac{2100}{3}$$ $$375x = 2 \times 700$$ $$375x = 1400$$

Both the numerator and the denominator are divisible by 25.

$$x = \frac{1400 \div 25}{375 \div 25}$$ $$x = \frac{56}{15}$$

The final answer is $\frac{56}{15}$.