I Have A Room That Is 432 Square Feet. How Many 18x18 Square Tiles Pieces Do I Need?

18 in = 1.5 ft
area of one tile, 18inx18in, =1.5ftx1.5ft= 2.25 ft2 /tile
432ft2/2.25ft2 /tile=192 tiles

But probably when you come to the wall you will have to cut a row of tiles to fit, so you will need extras.
How many extra tiles would depend on the actual dimensions of the room.
Suggestion; draw the plan of the room to scale and draw in lines to show the tiles. Then you can count them.

thanked the writer.
Anonymous commented
Another consideration is the shape of the room - does it have offsets, irregular shapes, etc. A square room is the simpliest to estimate but different shapes all have different answers, As Selkirk recommends, draw squares (actually I would recommend drawing a grid of 18 x 18 on a transparent sheet and laying that over a drawing of your room. From that you can adjust slightly to make the best fit, then count how many tiles you need. HINT - to look the best make each side piece equal.