My attempt at solution-:
Solution by a teacher-:
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up.Sign up to join this community
Your DFA doesn't match the empty string.
Note that if $L$ is regular, then infinitely many DFAs accept $L$. There is no unique answer for "DFA that accepts $L$". However, there is a canonical answer: there is a unique DFA with the minimum number of states that accepts $L$, known as the minimal DFA. Your teacher drew the minimal DFA for your language.
(Curiously, there is no "minimal NFA": there are regular languages for which there are several inequivalent NFAs with the minimum number of states.)