Both roll-up summary fields and after-save record-triggered flows can cause subsequent Data Manipulation Language (DML) operations within the same transaction, which in turn execute triggers on the affected records.

When a child record is modified, any roll-up summary field on the parent record is recalculated. This recalculation results in an update DML operation on the parent record, causing the parent object's triggers to fire.

Similarly, an after-save record-triggered flow executes after the initial record is saved. If this flow contains an action to update records (the same record or related ones), it initiates another DML operation, which will also fire the corresponding triggers. These subsequent operations increase the total count of trigger executions within the transaction.

1. Apex Developer Guide - Triggers and Order of Execution:

For C (Roll-up summary fields): "Executes roll-up summary fields. If the record contains a roll-up summary field or is part of a cross-object workflow

performs calculations and updates the roll-up summary field in the parent record. Parent record goes through save procedure." This explicitly states the parent record goes through the save procedure again

which includes firing its triggers.

For D (After-save record-triggered flow): "Executes record-triggered flows that are configured to run after the record is saved." These flows can perform DML

which will cause triggers to fire.

For A & B (Incorrect Options): The same document lists "Executes criteria-based sharing evaluation" and "Executes post-commit logic

such as sending email" as steps that occur after the primary trigger executions and do not initiate new DML within the core transaction.

Source: Salesforce

Apex Developer Guide

"Triggers and Order of Execution".

2. Salesforce Architects - Record-Triggered Automation Decision Guide:

For D (After-save record-triggered flow): This guide details that after-save flows are necessary "When you need to access the ID of the record that started the automation

or you need to update related records..." Updating related records is a DML operation that will fire triggers on those records.

Source: Salesforce Architects

Architect's Guide to Record-Triggered Automations

"When to Use an After-Save Flow".

3. Trailhead - Apex Triggers Module:

For C (Roll-up summary fields): The "Triggers and Order of Execution" unit explains that updates to a child in a master-detail relationship can cause the parent record to be updated due to a roll-up summary

which in turn fires the triggers on the parent object.

Source: Trailhead

Apex Triggers

"Triggers and Order of Execution" unit.