Using the Binomial Theorem for $(x + by)^n$:

The 2nd term $= \binom{n}{1}x^{n-1}(by) = nbx^{n-1}y$

Given the 2nd term is $8x^4y$: $n - 1 = 4 \Rightarrow n = 5$

$(x + by)^5$ expands to $5 + 1 = 6$ terms.

Since all terms have distinct powers of $x$, the total number of terms is $\mathbf{5}$ (after combining like terms, the $x^5$ through $x^0y^5$ terms, but the question asks for terms after expansion).