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Help with marginal rate of technical substitution!

I'm wondering how you determine the MRTS at a certain POINT on a graph. Point A is at 64 units of labor and 24 units of capital. So is the MRTS K/L? Which would be 0.375? Can someone help?!

The MRTS, by definition, is the number of units by which K can be reduced if an extra unit of L is used so that the output remains constant (i.e. you stay on the same isoquant), so K/L is incorrect.

The correct formula is:
-(change in K)/(change in L)
so the MRTS is just the absolute value of the slope of the isoquant when L is on the x-axis. When you want to evaluate the MRTS at a single point, the formula becomes a derivative:

For example, let's say the equation of your isoquant is
112 = L + 2*K
(you can verify that this passes through your point A). You can rewrite this as:
K = 56 - L/2
so dK/dL = -1/2
therefore, MRTS = -dK/dL = 1/2
Note: if -dK/dL is a function of either (or both) L and K, you need to plug in your original values into the equation to get the final numerical result.

Hope this helps.

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