Automata Theory

I did the DFA for the question below (see everything). However, my answer was not correct. I've given the solution to the question. I need a step by step explanation and labelling the intersection of DFA (example : look at the answer that I gave for letter j). Please show me how they got those two solutions. Thanks

Question and Solution:

My answer:

Same Question (different letter) and Solution:

My answer:

(j) Language L ={ wl w, contain at least two 0s and at most one 1} State diagram of DFA that recognizes L is given by: 0 0 0 0 0 0 0,1 29 2 0 6 {w | w contains an even number of 0s, or contain exactly two 1s) 0 0 0 0 0 0 e venO