To my surprise I didn't find the simplest solution in all the answers, so here it is. Referring to the question title Installing multiple packages in Ansible this is (using the yum module):

- name: Install MongoDB
  yum:
    name:
      - mongodb-org-server
      - mongodb-org-mongos
      - mongodb-org-shell
      - mongodb-org-tools 
    state: latest
    update_cache: true

Or with the apt module:

- name: Install MongoDB
  apt:
    pkg:
      - mongodb-org-server
      - mongodb-org-mongos
      - mongodb-org-shell
      - mongodb-org-tools 
    state: latest
    update_cache: true

Both modules support inline lists!

The second part of your question is how to integrate specific version numbers into the package lists. No problem - simply remove the state: latest (since using specific version numbers together with state: latest would raise errors) and add the version numbers to the package names using a preceding = like this:

- name: Install MongoDB
  yum:
    name:
      - mongodb-org-server=1:3.6.3-0centos1.1
      - mongodb-org-mongos=1:3.6.3-0centos1.1
      - mongodb-org-shell=1:3.6.3-0centos1.1
      - mongodb-org-tools=1:3.6.3-0centos1.1 
    update_cache: true

You could also optimize further and template the version numbers. In this case don't forget to add quotation marks :)

My solution is to merge these into one play, as they do the same thing.

---
- name: php-fpm play
  hosts: aws
  become: true
  vars:
  - repo:
      Debian:
      - apt # already installed, but need something here
      RedHat:
      - epel-release
  - packages:
      Debian:
      - apache2
      #- nginx # cannot have 2 listening on port 80
      - php-fpm
      RedHat:
      - httpd
      #- nginx
      - php-fpm
  - services:
      Debian: apache2
      RedHat: httpd

  tasks:
     # TODO move update * task to different play

   - name: Install repo
     # Seperate package transaction for EPEL
     # so it is available in the next task
     package:
       name: "{{ repo[ansible_os_family] }}"

   - name: Install Web Server Packages
     # Keyed by OS family fact to also support RHEL and Debian
     package:
       name: "{{ packages[ansible_os_family] }}"
       state: latest

   - name: Web Service Start
     service:
       name: "{{ services[ansible_os_family] }}"
       state: restarted
       enabled: yes

Can't have multiple servers listening on ports 80 and 443. I commented out nginx, as a task was mislabeled "Apache Service Start". If you want one of these proxying for the other or something, you will need to deploy a config file to change the ports.

Used the package: action which delegates to actual package manager. Enables a package install task to run on different OSes. Can't do update_cache that way, but yum doesn't need it when adding repos like apt does.

Vars structure is dicts of OS family specific values. This enables the package and service names to be indexed by facts. OS family, so this also works on RHEL and Debian in addition to CentOS and Ubuntu.

Indentation was wrong. Modules parameters need to be indented a level below task level directives like name:.

Can't include_tasks an entire play, that only works with import_playbook. include_tasks is easier when you have roles, which have a tasks directory for such files. (Play level tasks are a thing, but I am in favor of roles doing everything.)

There still is more work to make this useful.

When you need to use template to install configuration, EL puts configs in /etc/httpd/, while Debian is in /etc/apache2/.

Plenty of web server roles are open sourced, to look at if you want ideas. Check Galaxy.

Consider moving your tasks to roles, enables reuse.