DFA for w|w has a length multiple of 2 or 3 I am trying to create a DFA and a regex for this kind of exercise:

$A = \{w ∈ \{0, 1\}^* |\text{length of w is a multiple of 2 or 3}\}$. I tried to do one for $2$ and one for $3$ and then combine them, but it didn't seem to work cause I miss some cases for example $6,7$ or so. Any help would be gratefully received :D
Creating a state machine for each and combining the two is not a bad idea. To create a state machine accepting words having length N you can have each state represent the current length mod N.

After creating the two machines you can add a state having two epsilon transitions to the starting states of both machines. This gives a NFA accepting your language.

In a final stage you use the subset construction algorithm to convert the NFA you got into a DFA.