Given the hint 4 = 22, we substitute this into the expression:

The expression is $2^{224} \div 4^{32}$.
Given the hint $4 = 2^2$, we substitute this into the expression:

$$2^{224} \div (2^2)^{32}$$

Using the exponent rule $(a^m)^n = a^{mn}$:

$$(2^2)^{32} = 2^{2 \times 32} = 2^{64}$$

The expression becomes:

$$2^{224} \div 2^{64}$$

Using the exponent rule $a^m \div a^n = a^{m-n}$:

$$2^{224 - 64} = 2^{160}$$

We observe the pattern of the units digits of powers of 2:

• $2^1 = 2$
• $2^2 = 4$
• $2^3 = 8$
• $2^4 = 16 \implies 6$
• $2^5 = 32 \implies 2$ The pattern of units digits (2, 4, 8, 6) repeats every 4 powers. To find the units digit of $2^{160}$, we divide the exponent (160) by 4 and look at the remainder.

$$160 \div 4 = 40 \text{ with a remainder of } 0$$

When the remainder is 0, the units digit is the same as the units digit of $2^4$, which is 6.

The units digit in the value of $2^{224} \div 4^{32}$ is $\boxed{\text{6}}$.