Hey! Something that I can help with! I actually teach an intro to PLC course along with other Instrumentation courses.
There is a process to these problems that have a "floating zero" or "live zero" where your lowest value is not zero, but in this case 4 mA or 100 Deg C.
The trick is to convert the value to a percentage of the span first, staying in the given units, then multiply that percentage by the span of the new units and add the live zero back in.
So for this problem we would say our temperature span is 200 Deg C - 100 Deg C, for a total span of 100 Deg C. If you have 162 Deg C we could find the percentage of that span by subtracting the live zero and dividing by the span in that unit range:
(Given Value - Live Zero) / (Span) ==> (162 Deg C - 100 Deg C) / (100 Deg C) ==> 0.62 or 62% of our total span.
Now, if we want to relate that to a span of a different set of units we just have to work in reverse!
To find the Span of our new unit range (4 mA - 20 mA) we just have to take the largest value, and subtract the live zero.
Span = 20 mA - 4 mA = 16 mA
Now to relate our percentage of span from the original units of Deg C to our new unit range in mA:
(% of Span * New Span) + (Live Zero) ==> (62% * 16 mA ) + (4 mA) = 13.92 mA
Hope this helps!