По его взгляду трудно угадать, сердится он или просто устал.

Literally, по его взгляду means something like from his look or judging by his expression.

The preposition по often takes the dative case when it means by, from, or judging by. So:

• взгляд = look, gaze, expression
• взгляду = dative singular of взгляд

So the structure is:

• по + dative = from / by / judging by

That is why it is по его взгляду, not по его взгляд.

In this sentence, его means his, and this possessive form is normally indeclinable: it does not change for case, gender, or number.

So you get:

• его взгляд = his look
• по его взгляду = from his look
• с его взглядом = with his look

The noun changes, but его stays the same.

Here взгляд is best understood as look or expression, especially the look in someone’s eyes or face.

Depending on context, взгляд can mean:

• glance
• gaze
• look
• sometimes even viewpoint or opinion

But in this sentence, по его взгляду means you are judging from the way he looks, especially his facial expression or eyes.

Russian often uses an impersonal construction here:

• трудно угадать = hard to guess

English usually needs a dummy subject:

• It is hard to guess

Russian does not. So the sentence is literally closer to:

• From his look, hard to guess...

This is completely normal in Russian.

This is an aspect question.

• угадать = perfective
• угадывать = imperfective

Here the speaker means to figure out successfully in one instance: can you tell, or can you not tell, what is going on? That calls for the perfective угадать.

So трудно угадать means:

• it is hard to figure out
• it is hard to tell correctly

If you used угадывать, it would sound more like an ongoing or repeated process of guessing, which is not the idea here.

Not in the sense of making a random guess.

In this kind of sentence, угадать is often closer to:

• tell
• figure out
• read correctly
• make out

So трудно угадать here means it is hard to tell from his expression whether he is angry or just tired.

Because that part is a subordinate clause, more specifically an indirect question.

The sentence is structured like this:

• По его взгляду трудно угадать = From his look, it is hard to tell
• сердится он или просто устал = whether he is angry or just tired

Russian normally separates this kind of clause with a comma.

Both are possible, but сердится он sounds natural here because it keeps a slightly more question-like or contrastive feel.

Compare:

• сердится он или просто устал
• он сердится или просто устал

The second version is also grammatical, but the first one puts more focus on the alternatives:

• is he angry
• or just tired

So this word order is mostly about style and information structure, not a different basic meaning.

This is a very common point of confusion.

• сердится = he is angry / he is getting angry
• устал literally = he got tired, but very often in Russian it means he is tired as a present state resulting from becoming tired

So:

• сердится is a present-tense verb
• устал is a past form used with a resultative meaning

In English, we often translate both as present states:

• whether he is angry or just tired

Also, Russian often prefers устал over усталый when talking about someone’s temporary tiredness.

Because the alternatives are already stated clearly with или:

• сердится он или просто устал = whether he is angry or just tired

Russian often leaves out ли when the whether...or... meaning is already obvious from the structure.

A version with ли can exist in some contexts, but here the sentence sounds natural and normal without it.

Просто here means just or simply.

It softens the second possibility and sets up a contrast:

• maybe he is angry
• or maybe he is just tired

So просто устал suggests a simpler, less dramatic explanation.

Because the same subject applies to both parts:

• сердится он
• или просто устал

In English, we also usually do this:

• whether he is angry or just tired

Russian could repeat the pronoun for emphasis, but it is not necessary. One он is enough, and it naturally applies to both alternatives.