I had a little trouble understanding your question, but I think you're asking that the first parameter be the textbox text, and the second be the length of the textbox text. This I think should work:
MotherTongueTxtBox.Attributes.Add("onblur","val_Length(this.value,this.value.length)");
Remember that the above will render the html like:
<input type="text" onblur="val_Length(this.value, this.value.length)" />
In your original statement, the resulting (incorrect) html would have been something like:
<input type="text" onblur="val_Length(,0)"/>
Since MotherTongueTxtBox.Text and .Length would have been string.empty and 0 respectively (unless it already had initial values...)
EDIT:
Thanks for marking as solution. Just as a side note, one thing you may want to consider, is you don't need to pass this.value.length in as a parameter, since you're already passing in this.value. You could determine the length within your function. Just an idea though like this:
MotherTongueTxtBox.Attributes.Add("onblur","val_Length(this.value, 'Hi')");
And then in your javascript function:
function val_Length(value, myString) {
var length = value.length;
....
}