Show if this is valid or invalid (Propositional Logic) I just don't understand clearly what the question wants me to do?
It says:
Check if the following is valid or invalid
(I will take one question as an example.)
$$H\implies D $$
$$R\implies S$$
$$Therefore: (H \land  R \implies S \land D)$$
I understand that they want me to show a proof of this conclusion and also to show if this is valid. Just looking at it, it seems valid, but how do I prove it using natural laws of deduction (the logical way)? And just for information, I know all the laws of deduction. I just don't know how to apply them in situations like this.

There are many 'laws of deduction': there are many different systems of deduction, each of which with their own set of laws or rules ... so it would be good to know which rules you are allowed to use.
Nevertheless, here is a proof using fairly commonly used rules:

