La directora soltó una carcajada al ver la foto.

Because directora is the feminine form of director. It tells you the person is female.

• el director = a male director
• la directora = a female director

In Spanish, many job titles change form to match gender, and the article changes too.

Soltó is the preterite form of soltar.

The basic idea of soltar is to let go, to release, or to let out. With sounds, words, or reactions, it often means to let out something suddenly.

So:

• soltó una carcajada = she let out a loud laugh
• very natural English equivalent: she burst out laughing

This is a good example of Spanish using a verb more literally than English sometimes does.

It is an idiomatic and very common combination. Spanish often uses soltar with things that come out suddenly, especially reactions:

• soltar una risa
• soltar una carcajada
• soltar un grito
• soltar una respuesta

The feeling is that the laugh or reaction escaped suddenly and strongly.

Risa is the general word for laughter or a laugh.

Carcajada is stronger and more specific. It usually means:

• a loud laugh
• a sudden burst of laughter
• a big, hearty laugh

So una carcajada is more vivid than una risa.

Soltó is the preterite, which is used for a completed action viewed as a whole.

Here, the sentence describes a single event:

• she saw the photo
• she laughed

That is why soltó fits well.

If you used soltaba, it would suggest something more ongoing, habitual, or descriptive in the background, which does not match this sentence as naturally.

Al + infinitive is a very common Spanish structure meaning:

• when doing
• upon doing
• on seeing
• as soon as ... saw, depending on context

So al ver la foto means something like:

• when she saw the photo
• upon seeing the photo

It is a compact way to express the moment that triggered the laugh.

Because after al in this structure, Spanish uses the infinitive.

So the pattern is:

• al + infinitive

Examples:

• al entrar = when entering / upon entering
• al llegar = when arriving
• al ver = when seeing

You do not normally use a conjugated form like vio after al in this construction.

No. In al ver, the al does not refer to a masculine person or noun.

Here, al + infinitive is simply the structure used for when/upon doing. So even though the subject is la directora, you still say al ver, not anything different.

In other words, the gender of la directora has nothing to do with al here.

Normally, in a sentence like this, the person doing the action in al + infinitive is understood to be the same as the main subject.

So here, the natural reading is:

• the director saw the photo
• the director laughed

If Spanish wants to make it clear that a different person did the seeing, it usually uses a different structure.

Because Spanish usually uses an article with a noun in cases where English sometimes does not.

Here la foto means the photo. It probably refers to a specific photo already known in the situation or story.

Also, foto is a very common and fully standard short form of fotografía.

Yes. You could also say:

Al ver la foto, la directora soltó una carcajada.

This means the same thing. The difference is mainly one of emphasis and style:

• La directora soltó una carcajada al ver la foto = starts with the main action
• Al ver la foto, la directora soltó una carcajada = starts with the triggering event

Both are natural.