These fees are both expressed on an annual basis.
Consider a portfolio whose benchmark is cash (this is the norm for hedge funds). In one particular year, the benchmark return is 5%, and the portfolio gives a gross return of 20%. The base fee would be 2%. The performance fee would be 20% of the portfolio's active return. 20% of 15% is 3%. Therefore, the total fee for this portfolio in the specified year would be 5%.
Why should performance fees be calculated on the gross outperformance, when the investor can never obtain the gross performance (because they will at least be paying the base fee of 2%)? Under this arrangement, the fee calculation involves "double dipping". Specifically, the performance fee is being charged on 2% of the gross return that the investor will be paying as a base fee. One way of avoiding this "double dipping" is by subtracting the base fee from the gross return before calculating the performance fee. Some canny investment managers allow the investor to choose between (for example) 2+20 with double-dipping, or 2+24 without double-dipping. This is a smart tactic, because it gives the investor some feeling that they are controlling the fee level. However, whichever way you slice it, this is a very high level of fees to pay.