Dim words()
Dim v() = {"a", "e", "i", "o", "u", "y"}
Dim added As Boolean
words = txtAll.Lines()

For Each item In words
added = False
For i = 0 To 5
If item.ToString.StartsWith(v(i)) Then
txtVow.Text += item & vbNewLine
added = True
Exit For
End If
Next
If added = False Then
txtCon.Text += item & vbNewLine
End If
Next

Explanation:

In the first three lines, we create three variables. Words(), added, and v(). Next, we set v to include all vowels in the alphabet.
Because Words is an array-variable(it can hold multiple values) we can set it to include each row of the txtAll textbox.
We create a For Each-Next Loop to go through each word, and the first thing we do is to set added to false.
Because there are six vowels in the alphabet, we set a For-Next Loop from 0-5(which really means 1-6 but computers start counting at 0).
We then check if the current word starts with the current vowel. If it dos, we add it to the vowel textbox, set added to true to indicate that the word has been added.
We also exit the current loop, because we have already added the word.
Now we return to the first For Each-Next Loop.
If the item hasn't been added to the vowel textbox, we add it to the consonant one.
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