La franja horaria incluye una tarea pendiente.

Because the main noun is franja, and franja is feminine in Spanish. The article has to agree with the noun, so you say la franja.

The adjective also agrees with franja, which is why you get horaria and not horario.

So the pattern is:

• la franja
• la franja horaria

In Spain, franja horaria usually means a time slot, time band, or block of time in a schedule.

That is often more natural than using it for a geographical time zone. If you mean a geographical time zone, Spanish more commonly uses huso horario.

So in a scheduling context, franja horaria is a very natural choice.

Because horaria is an adjective here, and adjectives normally agree in gender and number with the noun they describe.

• franja = feminine singular
• so the adjective must also be feminine singular: horaria

Compare:

• un horario = a schedule/timetable (horario here is a noun)
• una franja horaria = a time slot (horaria here is an adjective)

That difference often confuses learners because horario can be either a noun or part of an adjective pair:

• horario / horaria

Incluye is the third-person singular present form of incluir.

The subject is la franja horaria, which is singular, so the verb must also be singular:

• la franja horaria incluye

If the subject were plural, the verb would change:

• Las franjas horarias incluyen...

Una introduces something non-specific or new in the sentence: one pending task, but not one already identified by both speakers.

So:

• una tarea pendiente = an unspecified pending task
• la tarea pendiente = a specific pending task that is already known or has been mentioned before

Using una is the more neutral choice if you are just stating that the time slot includes some pending task.

Here, pendiente is an adjective meaning still not done, outstanding, or pending.

So tarea pendiente means a task that still needs attention.

Be aware that pendiente has other meanings in other contexts, for example:

• un pendiente = an earring
• una pendiente = a slope
• estar pendiente de algo = to be keeping an eye on something / to be waiting on something

But in tarea pendiente, the meaning is clearly the adjective pending/outstanding.

Because in Spanish, descriptive adjectives usually come after the noun.

So the natural order is:

• tarea pendiente

This is the normal Spanish pattern. English often puts adjectives before the noun, but Spanish usually does the opposite.

Putting pendiente before the noun would sound unusual here and is not the normal phrasing.

Yes, that is grammatically possible, but incluye is more precise in this context.

• incluye suggests that the task is part of the time slot or schedule
• tiene is more general and can sound less exact

If you are talking about something being part of a plan, list, or schedule, incluye is often the better choice.

Because this is a normal direct object, and it is not a person.

Spanish uses the personal a mainly with specific people (and sometimes pets or personified beings). Since una tarea pendiente is a thing, not a person, you do not use a.

So:

• incluye una tarea pendiente ✔
• incluye a una tarea pendiente ✘

Yes, but the original order is the most neutral and natural.

The basic sentence is:

• La franja horaria incluye una tarea pendiente.

You could also say something like:

• Una tarea pendiente está incluida en la franja horaria.

That version is grammatical, but it sounds more formal or more focused on the task rather than the time slot.

So the original sentence is the most straightforward everyday wording.