If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number? 

Suppose that $x,y$ are any two numbers

Given that 40% of a number is equal to two-third of another number

It implies that $0.4x=\frac{2}{3}y$

Divide both sides by $0.4$

$\begin{array}{rcl}x& =& \frac{2}{3\left(0.4\right)}y\\ \frac{x}{y}& =& \frac{10}{6}\\ & =& \boxed{\frac{\mathbf{5}}{\mathbf{3}}}\end{array}$