I am giving you the transition table. Drawing DFA will be too unclear to understand.

The states are written in the form of Q_{(n}_{a%3)(nb%3)}.

Q_{00 }is the initial state. On getting 1 a we go to Q_{10. }Here the subscript has importance. It counts the mod value of a and b. When we give 1 a then n_{a}%3=1 and n_{b}%3=0.

Taking another example : Q_{20} is a state where n_{a}%3=2 and n_{b}%3=0. On getting another a it goes to Q_{00} because now the no. of a's has increased by 1 and n_{a}%3=0.

The states Q_{ab }with b>=a are the final states.

a | b | |

->*Q_{00} |
Q_{10} |
Q_{01} |

Q_{10} |
Q_{20} |
Q_{11} |

*Q_{01} |
Q_{11} |
Q_{02} |

Q_{20} |
Q_{00} |
Q_{21} |

*Q_{11} |
Q_{21} |
Q_{12} |

*Q_{02} |
Q_{12} |
Q_{00} |

Q_{21} |
Q_{01} |
Q_{22} |

*Q_{12} |
Q_{22} |
Q_{10} |

*Q_{22} |
Q_{02} |
Q_{20} |

Hopefully this table is okay..