Here is the table:

Japan                    South Korea
Steel     Autos           Steel     Autos
520          0              1200       0
500         600               900      400
350        1100             600        650
200         1300              200       800
 0           1430             0         810

Scetch the production possibilty schedule of 
Japan and South Korea.  Locate steel on the vertical axis
and autos on the horizontal axis of each nations graph.

a.  Why are the production possibilites schedules concave?

b.  In autarky (no trade) Japan's production and consumption 
points along its production possibiliyies schedule are assumed to be 
500 tons of steel and 600 autos.  Draw a line tangent to Japan's
autarky point, and from it, Calculate Japans MRT of steel into 
autos.  THIS IS WHERE I AM TOTALLY LOST!!!    In autarky South Korea 
production and consumption points along its production possibilites 
schedule are assumed to be 200 tons of steel and 800 autos.
Draw a line tangent To South Koreas autarky point  and from it
calculate
South Koreas MRT of of steel to autos.  AGAIN, TOTALLY LOST HERE!!!!!!

c.  Based on each nations MRT, should the two nations specialize
according
to the principle of comparative advantage?  If yes, in which product
should each nation specialize?

d.  With specialization suppose the MRT's of both countries converge 
at MRT =1.  Starting a Japan's autarky point,slide along its PPS until
the slope of the tangent line equals 1.  This becomes Japan's
production point
under partial specialization.  How many tons of steel and how many
autos will Japan produce at this point?  In like manner, determine
South Korea's production point under partial specialization.  How mant
tons of steel and how many autos will south Korea Produce?  For the
two nations, do their combined production of steel and autos with
partialspecialization exceed their output in the absence of
specialization? If so, by how much?  TOTALLY LOST HERE ONCE AGAIN.

With the relative product prices in each nation now in equilibrium at
1 ton of steel to 1 auto (MRT=1) suppose 500 autos are exchanged at
this terms of trade.
  1.  Determine the point along the Terms of trade line at which Japan
will locate after trade occurs.  What are Japan's consumption gains
from trade.
   2.  Determine the point along the terms of trade line at which
South Korea
will locate after trade occurs.  What are South Korea's consumption
gains from trade?

Briefly, the MRT is the marginal rate of transformation (e.g. how many
tonnes of steel Japan must give up/stop producing in order to
reallocate resources to auto production and gain 1 more auto). Hence
the MRT will be the gradient of the PPF (do it graphically if
necessary). I won't do all the calculation here, except for one
example:
if Japan is at (500,600) (steel,autos) and wishes to gain one more
auto, and we assume that the PPF is linear between (500,600) and
(350,1100) [which it WON'T be], then 150 tonnes of steel would be
given up to get 500 autos; hence the MRT = 150/500 = 0.3
Hence when the two nations trade, each will exploit their comparative
advantage and get to the point where their MRT's are equal.