Can you (do something)?

This is a "neutral" way of asking someone to do something. It's not super-polite but it's also not rude. In the example above, a mother uses this to ask her son to do the dishes. If the son wasn't always helpful, she might ask the question differently like this:

Anant, I want you to load up the dishwasher tonight.

And if the mother wanted to be really polite to him for some reason, she might ask:

Anant, would you mind loading up the dishwasher?

load up (something)

To "load up" something means to put stuff on or in it until it gets full. Aside from your dishwasher, some other things that you can "load up" include:

load up your truck

load up your plate (with food)

load up a basket

There's a very small difference between just using the word "load" and using "load up". When you say that someone "loaded" something, it makes me think of the action of them putting things on or in something. But when you say that they "loaded up" something, it makes me think of the result of having a full dishwasher, truck, bag, etc. However, the difference is small so you don't really need to worry about which word to use in most situations.