Yes, you can answer this question w/o a periodic table (in fact, a periodic table wouldn't help much with this). This question is asking if you have a basic understanding of the order in which electron shells are filled, and how many electrons occupy each atomic orbital.
So, in this example, you can immediately eliminate answers C and D because they both have d-orbitals with greater than 10 electrons (6d16, 5d14) - which is impossible. Then, for the remaining two answers, we can tell that answer B can't be correct as it states that the 6f orbitals come after the 6s orbital which is wrong (orbitals for a given electron shell go in the order of s,p,d,f). This leaves the only possible answer to be A.
Hope that helps.