How many half-lives must elapse until 84 % of a radioactive sample of atoms has decayed? -g?

Half-life is the time required for decay of 50% of radio-active nuclei.

Thus, when radio-active material crosses 1st half-life, 100/2 = 50% radio-active material is left and remaining 50% is elapsed.

When, when radio-active material crosses 2nd half-life, 50/2 = 25% radio-active material is left and remaining 75% is elapsed.

When radio-active material crosses 3rd half-life, 25/2 = 12.5% radio-active material is left and remaining 87.5% is elapsed.

Thus, 2 half-lives must elapse until 84 % of a radioactive sample of atoms has decayed.