So Hatach
Hathak (hath-awk')
Hathak, a Persian eunuch -- Hatach.
went forth
yatsa' (yaw-tsaw')
to go (causatively, bring) out, in a great variety of applications, literally and figuratively, direct and proxim.
to Mordecai
Mordkay (mor-dek-ah'-ee)
Mordecai, an Israelite -- Mordecai.
unto the street
rchob (rekh-obe')
a width, i.e. (concretely) avenue or area -- broad place (way), street.
of the city
`iyr (eer)
or (in the plural) par {awr}; or ayar (Judges 10:4) {aw-yar'}; a city (a place guarded by waking or a watch) in the widest sense (even of a mere encampment or post) -- Ai (from margin), city, court (from margin), town.
which was before
paniym (paw-neem')
the face (as the part that turns); used in a great variety of applications (literally and figuratively); also (with prepositional prefix) as a preposition (before, etc.)
the king's
melek (meh'-lek)
a king -- king, royal.
gate
sha`ar (shah'-ar)
an opening, i.e. door or gate -- city, door, gate, port (-er).