Turing decidable languages
Both $L_1$ and $L_2$ are decidable. Hence, they have algorithms $A_1$ and $A_2$ (respectively) that decide them.
Try to create a new turing machine (algorithm) using the two algorithms $A_1$ and $A_2$.
For example, for the union $L_1\cup L_2$, you can create the following algorithm:

run $A_1$ on the input. If it accepted, then also accept.
else, run $A_2$ on the input, and return what $A_2$ returned.