In a certain code language, 'RACE' is written as 'VWGA' and 'BANK' is written as 'FWRG'. How will 'STEM' be written in that code language?

Let's analyze the pattern by converting the letters to their alphabetical positional values ($A=1,B=2,\dots ,Z=26$):
**1. 'RACE' $\to$ 'VWGA':**

* $\text{R }(18)+4=\text{V }(22)$
* $\text{A }(1)-4=\text{W }(23)$ *(Note: $1-4=-3\equiv 26-3=23$)*
* $\text{C }(3)+4=\text{G }(7)$
* $\text{E }(5)-4=\text{A }(1)$

The pattern followed is alternating $+4$ and $-4$.

**2. 'BANK' $\to$ 'FWRG':**

* $\text{B }(2)+4=\text{F }(6)$
* $\text{A }(1)-4=\text{W }(23)$
* $\text{N }(14)+4=\text{R }(18)$
* $\text{K }(11)-4=\text{G }(7)$

3. Applying the same logic to 'STEM':

* $\text{S }(19)+4=\text{W }(23)$
* $\text{T }(20)-4=\text{P }(16)$
* $\text{E }(5)+4=\text{I }(9)$
* $\text{M }(13)-4=\text{I }(9)$

Therefore, 'STEM' is coded as 'WPII'.