What is the difference between the following networking terms (with an example if possible)?

Uni-cast :

Uni-cast is the term used to describe communication where a piece of information is sent from one point to another point. In this case there is just one sender, and one receiver.All LANs (e.g. Ethernet) and IP networks support the unicast transfer mode, and most users are familiar with the standard unicast applications (e.g. http, smtp, ftp and telnet) which employ the TCP transport protocol.

Broadcast:

Broadcast is the term used to describe communication where a piece of information is sent from one point to all other points. In this case there is just one sender, but the information is sent to all connected receivers.

Broadcast transmission is supported on most LANs (e.g. Ethernet), and may be used to send the same message to all computers on the LAN (e.g. the address resolution protocol (arp) uses this to send an address resolution query to all computers on a LAN). Network layer protocols (such as IPv4) also support a form of broadcast that allows the same packet to be sent to every system in a logical network (in IPv4 this consists of the IP network ID and an all1's host number).

Multicast:

Multicast is the term used to describe communication where a piece of information is sent from one or more points to a set of other points. In this case there is may be one or more senders, and the information is distributed to a set of receivers (there may be no receivers, or any other number of receivers).

The majority of installed LANs (e.g. Ethernet) are able to support the multicast transmission mode. Shared LANs (using hubs/repeaters) inherently support multicast, since all packets reach all network interface cards connected to the LAN. The earliest LAN network interface cards had no specific support for multicast and introduced a big performance penalty by forcing the adaptor to receive all packets (promiscuous mode) and perform software filtering to remove all unwanted packets. Most modern network interface cards implement a set of multicast filters, relieving the host of the burden of performing excessive software filtering.

Any cast:

In Internet Protocol Version6 (IPv6), anycast is communication between a single sender and the nearest of several receivers in a group. The term exists in contradistinction to multicast, communication between a single sender and multiple receivers, and unicast, communication between a single sender and a single receiver in a network.

Unicast -One to One Association, Communication between two intended recipients. 

The IP address would be the IP address for the intended MAC address of the destination.

EX: If you try to ping a System in your same subnet, the Packet will be forged with the destination IP address if the recipient.

ie- If you Ping your router or gateway, the packet will be send from the interface of your system to your switch or AC and will be redirected to the interface with the router /gateway has been connected.

Broadcast - One to many/ALL Communication between one and to many recipientsEX.If the destination Address is not available in the ARP table of the switch, the switch will send a Broadcast ARP packet using ARP protocol to ask 'who is..1.1' (gateway).

Broadcast Packet is where the destination IP Address will be...

This packet will reach all connected devices within a same network.

Multicast -One to Selected Many - Communication between one and selected/associated/unique many.

EX: one device will send packet to all its recipients at the same time.

One example will be while having voice or video conference.

Another example will be that all OSPF routers use.0.0.5 multicast address to send HELLO packet to its all OSPF routers in a subnet.

Anycast - One to the Nearest and available. Communication between one & one or many available recipients.

Unlike UNICAST MULTICAST BROADCAST, ANYCAST is methodlogy to broadcast IP to multiple recipients using dynamic routing protocols to its nearest recipients.

DNS is a anycast service.

Also is BGP neighbors will be made with the nearest and available BGP neighbors, and the routes also are selected and updated from and to the nearest neighbor.