To measure the average total effect of $X$ on $Y$, we need to measure the following two:

1. We can estimate the average causal effect (ACE) of a unit increase in $X$ on $M$ because the back-door path $X \leftarrow C \rightarrow Y \leftarrow M$ is blocked by the collider at $Y$. $ACE_{X \rightarrow M} = P(M|X) - P(M|no X)$
2. To measure the ACE of $M \rightarrow Y$, we can block the back-door path $M \leftarrow X \leftarrow C \rightarrow Y$ by controlling for $X$. $ACE_{M \rightarrow Y} = P(Y|do(M)) - P(Y|do(no M))$
3. According to the back-door adjustment formula: $P(A|do(B)) = \sum_{C} P(A|B, C=c)P(C=c)$

$\Rightarrow P(Y|do(X)) = \sum_{M} P(M=m|X) \sum_{X} P(Y|X=x,M=m)P(X=x) \Rightarrow ACE_{X \rightarrow Y} = ACE_{X \rightarrow M} * ACE_{M \rightarrow Y}$