They didn't reach an agreement their differences.
on account of
due. because
owing

They didn't reach an agreement on account of their differences.

Explanation:

In the given sentence, the necessary word(s) to be put in the blank will be suggestive of the 'cause' of the first part of the sentence. While the first part contains the effect' of the 'cause', completing the whole sentence depends on the part or parts of the phrase needed.

The given options "on account of", "due", "because" or "owing" are all valid to be used in the given sentence. But considering the form and structure of the sentence, the blank will be filled by "on account of".

To use the other options, we would need to add more to the already given words. We cannot simply write "they didn't reach an agreement due/owing/because their differences." For "due" and "owing", it needs "to" to make the sentence whole. Likewise, "because" requires "of" to be usable. If we add these words to the already given words, then the sentence can become

they didn't reach an agreement due to/ because of/ owing to their differences. But these options are wrong as the words are incomplete.

Thus, the correct answer is "on account of".

They didn't reach an agreement on account of their differences.

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his face was as red as an