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

Let's analyze the shifting pattern of alphabetical positions for the given words:
For **RACE $\to$ VWGA**:

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

For **BANK $\to$ FWRG**:

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

The common logic is an alternating pattern of $+4$ and $-4$.

Applying this pattern to STEM:

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

Thus, 'STEM' is written as WPII.