You are asked to build a multiple regression model but your model R² isn’t as good as you wanted. For improvement, you remove the intercept term now your model R² becomes 0.8 from 0.3. Is it possible? How?

Yes, it is possible.

• The intercept term refers to model prediction without any independent variable or in other words, mean prediction
  R² = 1 – ∑(Y – Y´)²/∑(Y – Ymean)² where Y´ is the predicted value.
• In the presence of the intercept term, R² value will evaluate your model with respect to the mean model.
  In the absence of the intercept term (Ymean), the model can make no such evaluation,
  With large denominator,
• Value of ∑(Y – Y´)²/∑(Y)² equation becomes smaller than actual, thereby resulting in a higher value of R².