JBARD |

The third letter first of 26 |
__A__ |

The fourth is eighth from the end R is eighth from Z |
__AR_ |

First is half the fourth plus one.
Half of R (18) = i + 1 = J |
J_AR_ |

The second next to the third, if A is third then it must be B |
JBAR_ |

The fifth is twice the second, 2 x 2 = 4
D is fourth in the alphabet |
JBARD |