1. **State the problem:** We need to find the value of $h$ such that $$4^8 \times 8^{12} = 2^h.$$\n\n2. **Rewrite the bases as powers of 2:**\n- $4 = 2^2$\n- $8 = 2^3$\n\n3. **Substitute these into the equation:**\n$$ (2^2)^8 \times (2^3)^{12} = 2^h.$$\n\n4. **Simplify the exponents using the power of a power rule $(a^m)^n = a^{mn}$:**\n$$ 2^{2 \times 8} \times 2^{3 \times 12} = 2^h,$$\nwhich simplifies to\n$$ 2^{16} \times 2^{36} = 2^h.$$\n\n5. **Use the product of powers rule $a^m \times a^n = a^{m+n}$:**\n$$ 2^{16 + 36} = 2^h,$$\nso\n$$ 2^{52} = 2^h.$$\n\n6. **Since the bases are equal, the exponents must be equal:**\n$$ h = 52.$$\n\n**Final answer:** $h = 52$