Q.Let X represent the difference between number of heads and number of tails obtained when a coin is tossed 6 times. What are possible values of X ?

A random variable is a real-valued function defined on the sample space of a random experiment: $X : S \to R$. Instead of tracking every raw outcome, it assigns a single real number to each outcome, letting us study numerical features of an experiment (like the number of heads, the sum on two dice, or the number of defectives) without carrying the full sample space along. Capital letters ($X, Y, Z$) name the random variable itself; a particular value it can take is written with a small letter $x$, and the set of all outcomes giving that value is the event $[X = x]$. The set of all values $X$ can take is called its range, and this range can be finite (e.g. $\{0,1,2,3\}$) or countably infinite (e.g. $\{1,2,3,\ldots\}$ when we count tosses until the first head).