How a switch works when it's aware of MAC address but the sending PC isn't aware of MAC of destination MAC

The ARP request will of course go through.

The switch doesn’t know about ARP. It only knows about Ethernet (ie. MAC addresses on Ethernet frames), not protocols on top of it. (Some switches offer advanced features like IGMP snooping, but that’s not relevant here.)

Because it’s a broadcast message, it has to be delivered to all (connected) ports. That’s all the switch cares about. It can’t know it’s really destined for computer D.

An ARP request is simply a message that says "You there at IP whatever! What's your MAC address?" Even though ARP deals with discovering layer 2 addresses, it's inherently a layer 3 request because it's being sent to an IP address. Switches don't operate at layer 3.

In the example you gave, you know something that the switch does not; that the IP address in the ARP request belongs to computer D. The destination MAC address is a broadcast and that's all the switch knows or cares about. If the switch sees a broadcast MAC, then it will broadcast that packet plain and simple.

Yes there are layer 3 switches out there, and pedants would point out that ARP technically isn't a layer 3 protocol, but none of that matters for this example.