Hint: Define the rational numbers first and try to find out any fractions in the form of $\dfrac{p}{q}$, where $q$ is not equal to 0, that are considered as rational numbers. So, between -1 and 2 there are an infinite number of rational numbers. Choose any out of them.
We have been asked in the question to find twelve rational numbers that lie between -1 and 2. So, before we start with that, we need to understand what rational numbers are. In mathematics, a rational number is defined as a number that can be expressed as the quotient or a fraction $\dfrac{p}{q}$ of two integers, where numerator is $p$ and the denominator $q$ is non-zero. Since $q$ may be equal to 1, every integer is a rational number. The set of all rational numbers are often referred to as ‘the rationals’. The field of rational numbers is usually denoted by a bold Q. It was thus denoted by Giuseppe Peano in 1895, after the Italian word, ‘quoziente’ meaning quotient. For example: $\dfrac{7}{3},2,1,\dfrac{5}{7}$ etc. The decimal expansion of a rational number either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over again. Moreover, any repeating or terminating decimal represents a rational number. For example: 0.25,0.5,0.8333 etc.
As we have been asked to find 12 rational numbers between -1 and 2, thus the numbers that can be considered as any of those 12 rational numbers could be, $\dfrac{-1}{9},\dfrac{-1}{8},\dfrac{-1}{7},\dfrac{-1}{6},\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},0,\dfrac{1}{6},1,\dfrac{3}{2},\dfrac{5}{2}$as they lie between -1 and 2 as a fraction in the form of $\dfrac{p}{q}$ where $q$ is not equal to 0.
Hence, the 12 rational numbers between -1 and 2 are, $\dfrac{-1}{6},\dfrac{-1}{7},\dfrac{-1}{8},\dfrac{-1}{9},0,\dfrac{1}{6},\dfrac{1}{4},\dfrac{1}{3},\dfrac{1}{2},1,\dfrac{3}{2},\dfrac{5}{2}$.