Let $X = \{1,2,3,4,5,6,l,m,b\}$ be a set.
Sample space is $\Omega = \{1,2,3,4,5,6\}^4$
$F = \{A \subset X | |A| = 4\}$ is the favourable event. Here,
1) Drawing $l$ with numbers represents the smallest number came twice. For example: drawing $\{1,2,3,l\}$ represents throwing $1,1,2,3$.
2) Drawing $m$ with numbers represents the middle number came twice. For example: drawing $\{1,2,3,m\}$ represents throwing $1,2,2,3$.
3) Drawing $b$ with numbers represents the biggest number came twice. For example: drawing $\{1,2,3,b\}$ represents throwing $1,2,3,3$.
4) Drawing $l,m$ with numbers represents the event that the smaller number repeats thrice. For example: drawing $\{1,2,l,m\}$ represents throwing $1,1,1,2$.
5) Drawing $b,m$ with numbers represents the event that the bigger number repeats thrice. For example: drawing $\{1,2,b,m\}$ represents throwing $1,2,2,2$.
6) Drawing $l,b$ with numbers represents the event that both numbers repeats twice. For example: drawing $\{1,2,l,b\}$ represents throwing $1,1,2,2$.
7) Drawing $l,b,m$ with a number represents the event where the number appears all the time. For example: drawing $\{1,m,l,b\}$ represents throwing $1,1,1,1$.
A little thought shows that this establishes a bijective map between this sample space and the actual events and thus $|F| = \binom{9}{4}$. Thus
$\Pr \{F\} = \dfrac{|F|}{|\Omega|} = \dfrac{126}{6^4} = \dfrac{7}{72}$