Regular Language to DFA conversion

Regular Language to DFA conversion

I ran into a problem in a textbook that I can't decipher and I was hoping
you could help. I'm not asking for a solution, just a translation, or a
push in the right direction. This is in the JFLAP textbook.
The alphabet consists only of "a".
{a^L |L = 0 (mod 6), L /= 0 (mod 4) }
Construct a DFA that recognizes this language.
I assume that if the string of a's is a multiple of 6 the string will be
accepted, but I don't really understand what L/= 0 would mean. There are
multiple questions like this.
Again, I don't need, or want, an answer to the problem, but maybe a
translation to an english sentence would help me to understand what they
are asking for.
Sincerely, Cory