To find the number of terms in the expansion of (x + y + 2z)^7, we can use the Binomial Theorem. According to the Binomial Theorem, the number of terms in the expansion of (a + b)^n is given by (n + 1).

In this case, we have (x + y + 2z)^7. Let's consider this as (a + b + c)^n, where a = x, b = y, c = 2z, and n = 7.

Using the Binomial Theorem, the number of terms in the expansion of (a + b + c)^n is (n + 1). Therefore, the number of terms in the expansion of (x + y + 2z)^7 is (7 + 1) = 8.

However, in this case, we need to consider the terms where the powers of x, y, and 2z add up to 7.

In the expansion of (x + y + 2z)^7, the powers of x, y, and 2z can range from 0 to 7.

Let's consider the terms where the powers of x, y, and 2z are 7, 0, and 0, respectively. This term can be written as x^7 * y^0 * (2z)^0 = x^7.

Similarly, we can consider the terms where the powers of x, y, and 2z are 6, 1, and 0, respectively. This term can be written as x^6 * y^1 * (2z)^0 = x^6 * y.

We can continue this process until we consider the terms where the powers of x, y, and 2z are 0, 0, and 7, respectively. This term can be written as x^0 * y^0 * (2z)^7 = (2z)^7.

Therefore, we have considered all the terms in the expansion of (x + y + 2z)^7.

Now, let's count the number of terms we have considered:

1. Term with x^7
2. Term with x^6 * y
3. Term with x^5 * y^2
4. Term with x^4 * y^3
5. Term with x^3 * y^4
6. Term with x^2 * y^5
7. Term with x * y^6
8. Term with y^7
9. Term with 2z^7

Therefore, the number of terms in the expansion of (x + y + 2z)^7 is 9, which is the correct answer.