I have a 2000 Acura TL that the bolts connecting the motor mount (or
engine mount i dont know which one, or if their is such a thing) to
the braket are both broken.  The mechanic said that it would cost
about $900 to fix it. He also said that i need to fix it because it is
flopping around and it will damage the engine, the transmission, and
some sort of rotating hing. My question is, can i just duct tape this
down to stop it from flopping all over and save myself $900? Thanks
for your help.

I would take his advice.  Duct tape is made to do just that, seal
ducts.  It will not mend supports for motors, withstand the constant
vibration.  And you probably can't apply duct tape in any way even to
do what you want.  The mechanic is telling you that if you don't get
it fixed properly, you are in for much more trouble.

Although I agree with myoarin, if you decide to try tape first,
there's a type of tape that has bamboo in it, wonderful stuff,
extremely strong.

I would get a second opinion/quote.Often shops exagurate the severity
to make the sell(it needs to get fixed). It's not a highly technical
job you should be able to get it done for A LOT LESS ($100-$300 plus
parts) from a non "shop" mechanic. You could check your local
newspapers classified for someone who would do it.

Consult an automotive welder. He might fix it for under $200 bucks.
Otherwise, if you're determined to do-it-yourself you might consider
using JB Weld instead of duct tape.

JBWELD
http://jbweld.net/index.php

Let me know if this worlks for you as an answser.

tutuzdad-ga