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Can I write this reaction $$\ce{A + B ->[\ce{X}] C + D ->[\ce{Y}] E + F}$$

as $$\ce{A + B ->[\ce{(1) X}][\ce{(2) Y}] E + F}$$

Can I write any organic reaction in this way or are there any conditions/rules?

Textbooks sometimes mention this form and sometimes they do not. What I have seen is that they mention mostly oxidation or reduction reactions this way but other reactions like addition are always presented in long form only. This answer describes a little bit but my question is a little different.

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It is depend on the reaction. For example, the given two reactions you have sighted are related to each other. It is a example of alkene to alcohol conversion using oxymercuration followed by demercuration with $\ce{NaBH4}$. The overall reaction is electrophilic addition of water to the alkene following Markovnikov's rule (when the nucleophile is water). The first reaction gives an organomercury intermediate, which is not important here for authors to mention. Yet, it is necessary to have a second reaction to convert carbon-mercury bond of the intermediate to carbon-hydrogen bond to get the product of interest. However, it is important to know (and is a common knowledge) that this intermediate should be isolated before treating it with $\ce{NaBH4}$ for following reasons:

  • One of the byproduct of reaction (1) is acetic acid, which violently react with $\ce{NaBH4}$.
  • One of the reactant of reaction (1) is water, which also react with $\ce{NaBH4}$.
  • The other reactant of reaction (1) is $\ce{Hg(OAc)2}$, which also react with $\ce{NaBH4}$.

Nonetheless, any chemist following this reaction sequence knows what hidden behind the sequence. It is also important to know that most organic reactions are written without byproducts, which are not important to the next step. To my understanding, it is okay to write two reaction sequence (even three or more) in a single reaction using steps (1) and (2) and more, as long as consequent intermediates are not important. For example, one of your intermediates $\ce{C}$ and $\ce{D}$ has to be a byproduct. But, if $\ce{C}$ and $\ce{D}$ give $\ce{E}$ and $\ce{F}$, respectively, reacting with $\ce{Y}$, you should show that in your sequence for readers benefits. I you are interesting only on $\ce{E}$ and $\ce{F}$ (together or you have a better separating method for the mixture), you can write it however you want it. The ball is always at your corner, but more explanatory way is always better.

Notes: Your first reaction doesnt make sense unless $\ce{Y}$ is a catalyst. If not, you should draw it as tri-component reaction: $$\ce{A + B + X -> C + D}$$ If it is a catalyst, then you can write it as: $$\ce{A + B ->[\text{cat. } \ce{X}] C + D}$$ An common example for this is: $$\ce{CH3CO2H + CH3CH2OH ->[\text{cat. } \ce{H2SO4}] CH3COOCH2CH3 + H2O}$$

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