In a certain code language, FORK is written as JKVG and COARSE is written as GKENWA. How will TERMITES be written in that language?

Let's analyze the pattern by looking at the positional values of the letters:
Case 1: FORK → JKVG

F(6)+4=J(10)

O(15)−4=K(11)

R(18)+4=V(22)

K(11)−4=G(7)
The pattern is alternating +4,−4,+4,−4.

Case 2: COARSE → GKENWA

C(3)+4=G(7)

O(15)−4=K(11)

A(1)+4=E(5)

R(18)−4=N(14)

S(19)+4=W(23)

E(5)−4=A(1)
The pattern +4,−4,+4,−4,+4,−4 is confirmed.

Applying the same logic to TERMITES:

T(20)+4=X(24)

E(5)−4=A(1)

R(18)+4=V(22)

I(9)−4=E(5) (Note: Looking at options, let's re-verify the middle letters sequence carefully. If we test M(13)+4=Q, but let's check options matching XAVIMPIO: T→X, E→A, R→V, M→I, I→M, T→P, E→I, S→O.)

Let's check the alternative cross-coding or position-based logic:
Divide TERMITES into pairs or halves:
Let's check Option B: XAVIMPIO

T(20)→X(24) (+4)

E(5)→A(1) (−4)

R(18)→V(22) (+4)

M(13)→I(9) (−4)

I(9)→M(13) (+4)

T(20)→P(16) (−4)

E(5)→I(9) (+4)

S(19)→O(15) (−4)

Thus, the exact sequential operation +4,−4,+4,−4,+4,−4,+4,−4 on TERMITES yields XAVIMPIO.