If $\text{MONKEY}$ is coded as $\text{OQPMGA}$ and $\text{ZEBRA}$ as $\text{BGDTC}$, then how will $\text{DEER}$ be coded?

Let's analyze the coding pattern by shifting the alphabetical positions:
Each letter is shifted forward by $+2$ positions.

$$\text{M}(+2)\to \text{O}$$

$$\text{O}(+2)\to \text{Q}$$

$$\text{N}(+2)\to \text{P}$$

$$\text{K}(+2)\to \text{M}$$

$$\text{E}(+2)\to \text{G}$$

$$\text{Y}(+2)\to \text{A}(\text{since }25+2=27\equiv 1)$$

Similarly for $\text{ZEBRA}\to \text{BGDTC}$.
Applying the same $+2$ shift rule to $\text{DEER}$:

$$\text{D}(+2)\to \text{F}$$

$$\text{E}(+2)\to \text{G}$$

$$\text{E}(+2)\to \text{G}$$

$$\text{R}(+2)\to \text{T}$$

The code is $\text{FGGT}$.