The answer is :

32

If we have to choose a number from natural numbers, then :

• Any number we choose say $x \gt 39$; if it is a multiple of 10, then it's also a multiple of 5. So as per rule no. $1$, it should be in the range $[1,19]$. So $x$ cannot be greater than $39$.
• But then, the only multiple of 10 (and 5) in the range as per rule 1, it should be 10. Then as per rule $2$, since $10$ is not a multiple of 8, it has to be in the range $[20,29]$. Thus, it causes a contradiction!
• And if we choose a number which is not a multiple of 10, then it has to be in the range $[30,39]$.
• Also, a point to note that if we do the same for rule $2$, i.e. choose a number which is not a multiple of $8$, then we need to make sure that it's a multiple of $10$ (by rule $3$). But by rule $1$, it's another contradiction.

Thus,

We need a number, which is in range $[30,39]$, a multiple of 8 and not a multiple of 5 or 10. So, $\{30,31,32,33,34,35,36,37,38,39\}$ we cancel : 30 , 35 , and the only acceptable number(multiple of $8$) left is $32$.

The answer is :

32

If we have to choose a number from natural numbers, then :

• Any number we choose say $x \gt 39$; if $x$ is a multiple of $10$, then $x$ also a multiple of $5$. So as per rule no. $1$, $x$ should be in the range $[1,19]$. So $x$ cannot be greater than $39$.
• But then, the only multiple of $10$ (and $5$) in the range as per rule $1$, $x$ should be 10. Then as per rule $2$, since $10$ is not a multiple of $8$, $x$ has to be in the range $[20,29]$. Thus, it causes a contradiction!
• And if we choose a number (this time $y$) which is not a multiple of $10$, then it has to be in the range $[30,39]$. (holding onto this branch for further possibilities...)
• Also, a point to note that if we do the same for rule $2$, i.e. choose a number $x$, which is not a multiple of $8$, then we need to make sure that $x$ is a multiple of $10$ (by rule $3$). But by rule $1$, it's another contradiction!!

Thus,

We need a number $y$, which is in range $[30,39]$, a multiple of 8 and not a multiple of 5 or 10. So, $\{30,31,32,33,34,35,36,37,38,39\}$ we cancel : 30 , 35 , and the only acceptable number(multiple of $8$) left is $32$.