The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is

 In a word ARTICLE, vowels are A, E, I and consonants are C, L, R, T.
In a seven letter word, there are three even places in which three vowels are placed in 3! way. In rest of the
four places, four consonants are placed in 4! ways.
.'. Required number of ways = $3!\times 4!=6\times 24=144$