Let \( x \) be the amount of money Anthony received for his birthday last year. According to the problem, we know that:
\[ 150 = \frac{x}{2} - 10 \]
To solve for \( x \), we first add 10 to both sides of the equation:
\[ 150 + 10 = \frac{x}{2} \] \[ 160 = \frac{x}{2} \]
Next, we multiply both sides by 2 to solve for \( x \):
\[ 160 \times 2 = x \] \[ x = 320 \]
So, the amount of money Anthony received for his birthday last year is
\[ \boxed{320} \]
To double-check our solution, we can verify it using the condition given in the problem. Half of \( 320 \) is \( 160 \). If we subtract \( 10 \) from \( 160 \), we get \( 150 \), which matches the amount he received this year. Therefore, the solution is correct, and Anthony received \( \boxed{320} \) last year.